Moving Charges and Magnetism Class 12 Notes: CBSE Physics Chapter 4

1. Force on a moving charge:

The source of the magnetic field is a moving charge.

Suppose a positive charge $\text{q}$ is in motion in a uniform magnetic field $\overset{\to }{\mathop{\text{B}}}\,$ with velocity $\overset{\to }{\mathop{\text{v}}}\,$ .

$\text{n}$ 

$\therefore \,\,\text{F}\,\text{ }\!\!\alpha\!\!\text{ }\,\text{qBvsin }\!\!\theta\!\!\text{ }\Rightarrow \text{F=kqBvsin }\!\!\theta\!\!\text{ }\,\,\left[ \text{k}=\text{constant} \right]$ 

Where in S.I. system, $\text{k}=1$ 

$\therefore \,\,\text{F=qBsin }\!\!\theta\!\!\text{ }\,\,\text{and}\,\,\overset{\to }{\mathop{\text{F}}}\,\text{=q}\left( \overset{\to }{\mathop{\text{v}}}\,\times \overset{\to }{\mathop{\text{B}}}\, \right)$ 

2. Magnetic field strength $\left( \overset{\to }{\mathop{\text{B}}}\, \right)$ :

We can see that in the equation,

$\text{F}=\text{qBvsin }\!\!\theta\!\!\text{ }$, if $\text{q}=1,\,\text{v}=1$,

$\text{sin }\!\!\theta\!\!\text{ }=1$ i.e. $\text{ }\!\!\theta\!\!\text{ }={{90}^{\circ }}$ then $\text{F}=\text{B}$.

Therefore magnetic field strength can be known as the force felt by a unit charge in motion with unit velocity perpendicular to the direction of the magnetic field.

There are some special cases for this:

1. If $\text{ }\!\!\theta\!\!\text{ }={{0}^{\circ }}$ or

${{180}^{\circ}}$, $\text{sin }\!\!\theta\!\!\text{ =0}$ 

$\therefore \,\,\text{F}=0$ 

A charged particle that is in motion parallel to the magnetic field will be not experiencing any force.

2. When $\text{v}=0,\text{F}=0$ 

At rest, a charged particle in a magnetic field will be not experiencing any force.

3. When $\text{ }\!\!\theta\!\!\text{ }={{90}^{\circ }}$, $\text{sin }\!\!\theta\!\!\text{ }=1$ then the force will be maximum

${{\text{F}}_{\text{max}\text{.}}}=\text{qvB}$ 

A charged particle in a motion perpendicular to the magnetic field will be experiencing maximum force.

3. S.I. unit of magnetic field intensity: 

The S.I unit has been found to be tesla (T).

$\text{B}=\frac{\text{F}}{\text{qvsin }\!\!\theta\!\!\text{ }}$ 

When $\text{q}=1\text{C},\,\text{v}=\text{1m/s},\,\text{ }\!\!\theta\!\!\text{ }={{90}^{\circ }}$ That is, $\text{sin }\!\!\theta\!\!\text{ }=1$ and $\text{F}=\text{1N}$ 

Then $\text{B}=\text{1T}$.

At a point, the strength of the magnetic field can be called as \[\text{1T}\] if a charge of \[\text{1C}\] which have a velocity of $1$ m/s while in motion at the right angle to a magnetic field experiences a force of \[\text{1N}\] at that point.

4. Biot-Savart’s law:

The strength of magnetic flux density or magnetic field at a point \[\text{P}\](dB) because of the current element \[\text{dl}\] will be dependent on,

1. $\text{dB}\,\text{ }\!\!\alpha\!\!\text{ }\,\text{I}$ 

2. $\text{dB}\,\text{ }\!\!\alpha\!\!\text{ }\,\text{dl}$ 

3. $\text{dB}\,\text{ }\!\!\alpha\!\!\text{ }\,\text{sin }\!\!\theta\!\!\text{ }$ 

4. $\text{dB}\,\text{ }\!\!\alpha\!\!\text{ }\,\frac{\text{1}}{{{\text{r}}^{\text{2}}}}$,

When we combine them, $\text{dB}\,\text{ }\!\!\alpha\!\!\text{ }\,\frac{\text{Idlsin }\!\!\theta\!\!\text{ }}{{{\text{r}}^{\text{2}}}}\Rightarrow \text{dB=k}\frac{\text{Idlsin }\!\!\theta\!\!\text{ }}{{{\text{r}}^{\text{2}}}}$         [$\text{k}=$Proportionality constant]

In S.I. units, $\text{k}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}}{\text{4 }\!\!\pi\!\!\text{ }}$ where ${{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}$ can be called as permeability of free space.

${{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}=\text{4 }\!\!\pi\!\!\text{ }\times \text{1}{{\text{0}}^{\text{-7}}}\,\text{T}{{\text{A}}^{\text{-1}}}\text{m}$ 

$\therefore \,\,\text{dB}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}}{\text{4 }\!\!\pi\!\!\text{ }}\frac{\text{Idlsin }\!\!\theta\!\!\text{ }}{{{\text{r}}^{\text{2}}}}$ and \[\overset{\to }{\mathop{\text{dB}}}\,=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}}{\text{4 }\!\!\pi\!\!\text{ }}\text{I}\frac{\left( \overset{\to }{\mathop{\text{dl}}}\,\times \overset{\to }{\mathop{\text{r}}}\, \right)}{{{\text{r}}^{\text{3}}}}\] 

$\overset{\to }{\mathop{\text{dB}}}\,$ will be perpendicular to the plane containing $\overset{\to }{\mathop{\text{dl}}}\,$ and $\overset{\to }{\mathop{\text{r}}}\,$ and will be directed inwards.

5. Applications of Biot-Savart’s law:

• Magnetic field $\left( \text{B} \right)$ kept at the Centre of a Current Carrying Circular Coil of radius $r$.

$\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{I}}{\text{2r}}$

If there are $n$ turns, then the magnetic field at the centre of a circular coil of n turns will be,

$\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{nI}}{\text{2r}}$ 

Here \[\text{n}\] will be the number of turns of the coil. \[\text{I}\] will be the current in the coil and \[\text{r}\] will be the radius of the coil.

• Magnetic field because of a straight conductor carrying current.

$\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{I}}{\text{4 }\!\!\pi\!\!\text{ a}}\left( \sin {{\phi }_{2}}+\sin {{\phi }_{1}} \right)$ 

Here \[\text{a}\] will be the perpendicular distance of the conductor from the point where the field is to the measured.

${{\phi }_{1}}\,\,\text{and}\,\,{{\phi }_{2}}$ will be the angles created by the two ends of the conductor with the point.

In case of an infinitely long conductor, ${{\phi }_{1}}={{\phi }_{2}}=\frac{\text{ }\!\!\pi\!\!\text{ }}{\text{2}}$ 

$\therefore \,\,\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}}{\text{4 }\!\!\pi\!\!\text{ }}\text{.}\frac{\text{2I}}{\text{a}}$ 

• At a point on the axis, magnetic field of a Circular Coil Carrying Current.

If point \[\text{P}\] is lying far away from the centre of the coil.

$\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}}{\text{4 }\!\!\pi\!\!\text{ }}\frac{\text{2M}}{{{\text{x}}^{\text{3}}}}$ 

Where $\text{M}=\text{nIA}=\text{magnetic}\,\text{dipole}\,\text{moment}\,\text{of}\,\text{the}\,\text{coil}$.

$\text{x}$ be the distance of the point where the field is needed to be measured, \[\text{n}\] be the number of turns, \[\text{I}\] be the current and \[\text{A}\] be the area of the coil.

• Magnetic field at the centre of a semi-circular current-carrying conductor will be,

$\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{I}}{\text{4a}}$

• Magnetic field at the centre of an arc of circular current-carrying conductor which is subtending an angle 0 at the centre will be,

$\text{B=}\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{I }\!\!\theta\!\!\text{ }}{\text{4 }\!\!\pi\!\!\text{ a}}$

6. Ampere’s circuital law:

Around any closed path in vacuum line integral of magnetic field \[\overset{\to }{\mathop{\text{B}}}\,\] will be ${{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}$ times the total current through the closed path. that is, $\oint{\overset{\to }{\mathop{\text{B}}}\,\text{.}\overset{\to }{\mathop{\text{dl}}}\,}={{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{I}$ 

7. Application of Ampere’s circuital law:

1. Magnetic field because of a current carrying solenoid, $\text{B}={{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{nI}$ 

$\text{n}$ be the number of turns per unit length of the solenoid.

In the edge portion of a short solenoid, $\text{B}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{nI}}{\text{2}}$ 

2.  Magnetic field because of a toroid or endless solenoid

$\text{B}={{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}\text{nI}$ 

8. Motion in uniform electric field of a charged particle:–

Parabola is the path of a charged particle in an electric field.

Equation of the parabola be ${{\text{x}}^{\text{2}}}=\frac{\text{2m}{{\text{v}}^{\text{2}}}}{\text{qE}}\text{y}$ 

Where $\text{x}$ be the width of the electric field.

$\text{y}$ be the displacement of the particle from its straight path.

$\text{v}$ be the speed of the charged particle.

$\text{q}$ be the charge of the particle

$\text{E}$ be the electric field intensity.

$\text{m}$ be the mass of the particle.

9. In a magnetic field $(\overset{\to }{\mathop{B}}\,)$ which is uniform, the path of a particle which is charged in motion with a velocity $\overset{\to }{\mathop{\text{v}}}\,$ creating an angle $\text{ }\!\!\theta\!\!\text{ }$ with $\overset{\to }{\mathop{\text{B}}}\,$ will be a helix.

The component of velocity \[\text{vcos }\!\!\theta\!\!\text{ }\] will not be given a force to the charged particle, hence under this velocity in the direction of \[\overset{\to }{\mathop{\text{B}}}\,\], the particle will move forward with a fixed velocity. The other component $\text{vsin }\!\!\theta\!\!\text{ }$ will create the force $\text{F}=\text{qBvsin }\!\!\theta\!\!\text{ }$, which will be supplying the needed centripetal force to the charged particle in the motion along a circular path having radius $\text{r}$.

$\because \,\,\text{Centripetal}\,\text{force}=\frac{\text{m}{{\left( \text{vsin }\!\!\theta\!\!\text{ } \right)}^{\text{2}}}}{\text{r}}=\text{Bqvsin }\!\!\theta\!\!\text{ }$ 

$\therefore \,\,\text{vsin }\!\!\theta\!\!\text{ }=\frac{\text{Bqr}}{\text{m}}$ 

Angular velocity of rotation$=\text{w=}\frac{\text{vsin }\!\!\theta\!\!\text{ }}{\text{r}}=\frac{\text{Bq}}{\text{m}}$ 

Frequency of rotation\[=\text{v}=\frac{\text{ }\!\!\omega\!\!\text{ }}{\text{2 }\!\!\pi\!\!\text{ }}=\frac{\text{Bq}}{\text{2 }\!\!\pi\!\!\text{ m}}\] 

Time period of revolution$=\text{T=}\frac{\text{1}}{\text{v}}=\frac{\text{2 }\!\!\pi\!\!\text{ m}}{\text{Bq}}$ 

10. Cyclotron: 

This can be defined as a device we use for accelerating and therefore energize the positively charged particle. This can be created by keeping the particle, in an oscillating perpendicular magnetic field and a electric field. The particle will be moving in a circular path.

$\therefore \,\,\,\text{Centripetal}\,\text{force}=\text{magnetic}\,\text{Lorentz}\,\text{force}$ 

$\Rightarrow \frac{\text{m}{{\text{v}}^{\text{2}}}}{\text{r}}=\text{Bqv}\Rightarrow \frac{\text{mv}}{\text{Bq}}=\text{r}$ $\leftarrow $ radius of the circular path

Time for travelling a semicircular path$=\frac{\text{ }\!\!\pi\!\!\text{ r}}{\text{v}}=\frac{\text{ }\!\!\pi\!\!\text{ m}}{\text{Bq}}=\text{constant}$.

When ${{\text{v}}_{\text{0}}}$ be the maximum velocity of the particle and ${{\text{r}}_{\text{0}}}$ be the maximum radius of its path then we can say that,

$\frac{\text{mv}_{\text{0}}^{\text{2}}}{{{\text{r}}_{\text{0}}}}=\text{Bq}{{\text{v}}_{\text{0}}}\Rightarrow {{\text{v}}_{\text{0}}}=\frac{\text{Bq}{{\text{r}}_{\text{0}}}}{\text{m}}$ 

Maximum kinetic energy of the particle$=\frac{\text{1}}{\text{2}}\text{mv}_{\text{0}}^{\text{2}}=\frac{\text{1}}{\text{2}}\text{m}{{\left( \frac{\text{Bq}{{\text{r}}_{\text{0}}}}{\text{m}} \right)}^{\text{2}}}\Rightarrow {{\left( \text{K}\text{.E}\text{.} \right)}_{\text{max}\text{.}}}=\frac{{{\text{B}}^{\text{2}}}{{\text{q}}^{\text{2}}}\text{r}_{\text{0}}^{\text{2}}}{\text{2m}}$ 

Time period of the oscillating electric field$\Rightarrow \text{T}=\frac{\text{2 }\!\!\pi\!\!\text{ m}}{\text{Bq}}$.

Time period be the independent of the speed and radius.

Cyclotron frequency $=\text{v}=\frac{\text{1}}{\text{T}}=\frac{\text{Bq}}{\text{2 }\!\!\pi\!\!\text{ m}}$ 

Cyclotron angular frequency$={{\text{ }\!\!\omega\!\!\text{ }}_{\text{0}}}=\text{2 }\!\!\pi\!\!\text{ v}=\frac{\text{Bq}}{\text{m}}$

11. Force acting on a current carrying conductor kept in a magnetic field will be,

\[\overset{\to }{\mathop{\text{F}}}\,=\text{I}\left| \overset{\to }{\mathop{\text{l}}}\,\times \overset{\to }{\mathop{\text{B}}}\, \right|\] or $\text{F}=\text{IlBsin }\!\!\theta\!\!\text{ }$ 

Here $\text{I}$ be the current through the conductor

$\text{B}$ be the magnetic field intensity.

$\text{l}$ be the length of the conductor.

$\text{ }\!\!\theta\!\!\text{ }$ be the angle between the direction of current and magnetic field.

1. If $\text{ }\!\!\theta\!\!\text{ }={{0}^{\circ }}$ or ${{180}^{\circ }}$, $\text{sin }\!\!\theta\!\!\text{ }\Rightarrow 0\Rightarrow \text{F}=0$ 

$\therefore $  If a conductor is kept along the magnetic field, no force will be acting on the conductor.

2. If $\text{ }\!\!\theta\!\!\text{ }={{90}^{\circ }}$, $\text{sin }\!\!\theta\!\!\text{ }=1$, $\text{F}$ will be maximum.

${{\text{F}}_{\text{max}}}\text{=IlB}$ 

If the conductor has been kept normal to the magnetic field, it will be experiencing maximum force.

12. The force between two parallel current-carrying conductors:–

1.  If the current will be in a similar direction the two conductors will be attracting each other with a force

$\text{F}=\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{\text{0}}}}{\text{4 }\!\!\pi\!\!\text{ }}.\frac{\text{2}{{\text{I}}_{\text{1}}}{{\text{I}}_{\text{2}}}}{\text{r}}$ per unit length of the conductor

2.  If the current is in opposite direction the two conductors will be repelling each other with an equal force.

3.  S.I. unit of current is \[1\] ampere. \[\left( \text{A} \right)\text{.}\] 

$\text{1A}$ can be defined as the current which on flowing through each of the two parallel uniform linear conductor kept in free space at a distance of $\text{1m}$ from each other creates a force of $\text{2 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-7}}}\,\text{N/m}$ along their lengths.

13. Torque experienced on a current carrying coil kept in a magnetic field:

$\overset{\to }{\mathop{\tau }}\,=\overset{\to }{\mathop{\text{M}}}\,\times \overset{\to }{\mathop{\text{B}}}\,\Rightarrow \tau =\text{MBsin }\!\!\alpha\!\!\text{ }=\text{nIBAsin }\!\!\alpha\!\!\text{ }$ where $\text{M}$ be the magnetic dipole moment of the coil.

 $\text{M}=\text{nIA}$ 

 Where $\text{n}$ be the number of turns of the coil.

 $\text{I}$ be the current through the coil.

 $\text{B}$ be the intensity of the magnetic field.

 \[\text{A}\] be the area of the coil.

\[\text{ }\!\!\alpha\!\!\text{ }\] will be the angle in between the magnetic field $\left( \overset{-}{\mathop{\text{B}}}\, \right)$ and normal to the plane of the coil.

Special Cases will be:

1. When the coil has been kept parallel to magnetic field $\text{ }\!\!\theta\!\!\text{ }={{0}^{\circ }}$, $\text{cos }\!\!\theta\!\!\text{ }=1$ then torque will be maximum.

${{\text{ }\!\!\tau\!\!\text{ }}_{\text{max}\text{.}}}=\text{nIBA}$ 

2. When the coil is kept perpendicular to magnetic field, $\text{ }\!\!\theta\!\!\text{ }={{90}^{\circ }}$, $\text{cos }\!\!\theta\!\!\text{ }=0$ 

$\therefore \,\,\text{ }\!\!\tau\!\!\text{ }=0$ 

14. Moving coil galvanometer:

This has been on the basis on the principle that if a coil carrying current has been kept in a magnetic field it is experiencing a torque. There is a restoring torque because of the phosphor bronze strip which is bringing back the coil to its normal position.

In equilibrium,

\[\text{Deflecting torque }=\text{ Restoring torque}\] 

$\text{nIBA}=\text{k }\!\!\theta\!\!\text{ }$ [$\text{k}=\text{restoring torque/unit twist of the phosphor bronze strip}]\text{ }$ 

$\text{I}=\frac{\text{k}}{\text{nBA}}\text{ }\!\!\theta\!\!\text{ }=\text{G }\!\!\theta\!\!\text{ }$  where $\text{G}=\frac{\text{k}}{\text{nBA}}=\text{Galvanometer}\,\,\text{constant}$ 

$\therefore \,\,\text{I}\,\text{ }\!\!\alpha\!\!\text{ }\,\text{ }\!\!\theta\!\!\text{ }$ 

Current sensitivity of the galvanometer can be defined as the deflection made if the unit current has been passed through the galvanometer.

${{\text{I}}_{\text{s}}}=\frac{\text{ }\!\!\theta\!\!\text{ }}{\text{I}}=\frac{\text{nBA}}{\text{k}}$ 

Voltage sensitivity can be explained as the deflection created if unit potential difference has been applied across the galvanometer.

${{\text{V}}_{\text{s}}}=\frac{\text{ }\!\!\theta\!\!\text{ }}{\text{V}}=\frac{\text{ }\!\!\theta\!\!\text{ }}{\text{IR}}=\frac{\text{nBA}}{\text{kR}}$ $\left[ \text{R = Resistance of the galvanometer} \right]$ 

15. The maximum sensitivity of the galvanometer is having some conditions:- 

The galvanometer has been defined to be sensitive if a small current develops a large deflection.

$\because \,\,\text{ }\!\!\theta\!\!\text{ }=\frac{\text{nBA}}{\text{k}}\text{I}$ 

$\because \,\,\text{ }\!\!\theta\!\!\text{ }$ will be large if (i) $\text{n}$ is large, (ii) $\text{B}$ is large (iii) $\text{A}$ is large and (iv) $\text{k}$ is small.

16. Conversion of galvanometer into voltmeter and ammeter:

1. A galvanometer has been converted to voltmeter by putting a high resistance in series with it.

\[\text{Total resistance of voltmeter }=\text{ }{{\text{R}}_{\text{g}}}\text{ + R}\] where ${{\text{R}}_{\text{g}}}$ be the galvonometer resistance.

$\text{R}$ be the resistance added in series.

Current through the galvanometer$={{\text{I}}_{\text{g}}}=\frac{\text{V}}{{{\text{R}}_{\text{g}}}\text{+R}}$ 

Here $\text{V}$ is the potential difference across the voltmeter.

$\therefore \,\,\text{R}=\frac{\text{V}}{{{\text{I}}_{\text{g}}}}-\text{G}$ 

Range of the voltmeter: \[0\text{V volt}\text{. }\] 

2. A galvanometer can be converted into an ammeter by the connection of a low resistance in parallel with it (shunt)

$\text{Shunt}=\text{S}=\left( \frac{{{\text{I}}_{\text{g}}}}{\text{I}-{{\text{I}}_{\text{g}}}} \right){{\text{R}}_{\text{g}}}$ where ${{\text{R}}_{\text{g}}}$ be the galvanometer’s resistance.

$\text{I}$ be the total current through the ammeter.

${{\text{I}}_{\text{g}}}$  be the current through the ammeter. 

Effective resistance of the ammeter will be,

$\text{R}=\frac{{{\text{R}}_{\text{g}}}}{{{\text{R}}_{\text{g}}}+\text{S}}$ 

The range of the ammeter will be $0-\text{IA}$. An ideal ammeter will be having zero resistance.

Moving Charges and Magnetism Class 12 Notes Physics - Basic Subjective Questions

Section-A (1 Marks Questions)

1. Is any work done on a moving charge by a magnetic field?

Ans. Since the magnetic force is perpendicular to the displacement of the moving charge, therefore the work done by the magnetic force is zero.

2. What is the gyromagnetic ratio?

Ans. Gyromagnetic ratio of an electron is the ratio of its magnetic moment to its orbital angular momentum.

$\mu _{l}=\dfrac{e}{2m_{c}}l$

μl is the magnetic moment of the electron, l is the oriental angular momentum of the electron.

$g(gyromagnetic\;ratio)=\dfrac{\mu _{l}}{l}=\dfrac{e}{2m_{c}}$

3. If the magnetic field is parallel to the positive y-axis and the charged particle is moving along the positive x-axis, which way would the Magnetic force be for :

(a) an electron (negative charge), 

(b) a proton (positive charge)?  

Ans.

(a) For electron, the force will be along –z axis;

(b) For a positive charge (proton), the force is along the +z axis.

4. Why should the spring/suspension wire in a moving coil galvanometer have a low torsional constant?

Ans. Low torsional constant is basically required to increase the current/charge sensitivity in a moving coil ballistic galvanometer.

5. State one limitation of Ampere’s Circuital Law.

Ans. Ampere’s Circuital Law is only valid for steady currents. If the current changes with time then Ampere’s Circuital Law is not applicable.

Section – B (2 Marks Questions)

6. State two properties of the material of the wire used for suspension of the coil in a moving coil galvanometer?

Ans. Two properties of the material of the wire used for suspension of the coil in a moving coil galvanometer

(a) Non - Brittle conductor

(b) Restoring Torque per unit Twist should be small.

7. Two wires of equal lengths are bent in the form of two loops. One of the loops is square shaped whereas the other loop is circular. These are suspended in a uniform magnetic field and the same current is passed through them. Which loop will experience greater torque? Give reasons?

Ans. We know that, Torque = NAIB

Since the area of circular loops is more than of a square loop torque experienced by a circular loop is greater.

8. A cyclotron is not suitable to accelerate electrons. Why?

Ans. A cyclotron is not suitable to accelerate electrons because its mass is less due to which they gain speed and step out of the dee immediately.

9. Write the two measures that can be taken to increase the sensitivity of a galvanometer.

Ans. Measures that can be taken to increase the sensitivity of a galvanometer,

• Increasing the no. of turns and the area of the coil,

• Increasing the magnetic induction and,

• Decreasing the couple per unit twist of the suspension wire.

• 
  

10. Write the condition under which an electron will move undeflected in the presence of crossed electric and magnetic fields.

Ans. The electric field and magnetic field should be perpendicular to each other. The velocity of the moving charge should be, v = E/B.

Important Formulas of Class 12 Chapter 4 Physics You Shouldn’t Miss!

Here are the important formulas for Class 12 Physics Chapter 4: Moving Charges and Magnetism that you shouldn’t miss:

1. Magnetic Field Due to a Current-Carrying Conductor:

- Straight Current-Carrying Conductor: $ B = \frac{{\mu_0 I}}{{2 \pi r}} $

- where $ B $ is the magnetic field, $ \mu_0 $ is the permeability of free space ($4 \pi \times 10^{-7} \, \text{T m/A}$), $ I $ is the current, and $r$ is the distance from the conductor.

2. Magnetic Field Due to a Current in a Circular Loop:

- At the Center of the Loop: $ B = \frac{{\mu_0 I}}{{2 r}} $

- where $ r $ is the radius of the loop.

3. Ampere’s Circuital Law:

- $ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enclosed}} $

- where $ \oint \vec{B} \cdot d\vec{l} $ is the line integral of the magnetic field around a closed loop, and $ I_{\text{enclosed}} $ is the current enclosed by the loop.

4. Magnetic Field Due to a Solenoid:

   - Inside the Solenoid: $ B = \mu_0 n I $

  - where $ n $ is the number of turns per unit length of the solenoid.

5. Force on a Moving Charge in a Magnetic Field:

- $ F = q v B \sin \theta $

- where $ F $ is the force, $ q $ is the charge, $ v $ is the velocity of the charge, $ B $ is the magnetic field strength, and $ \theta $ is the angle between the velocity and the magnetic field.

6. Force on a Current-Carrying Conductor in a Magnetic Field:

- $ F = I l B \sin \theta $

- where $ l $ is the length of the conductor in the magnetic field, and $ \theta $ is the angle between the current direction and the magnetic field.

7. Magnetic Flux:

- $ \Phi = B A \cos \theta $

- where $ \Phi $ is the magnetic flux, $ B $ is the magnetic field strength, $ A $ is the area through which the magnetic field lines pass, and $ \theta $ is the angle between the magnetic field and the normal to the surface.

8. Electromagnetic Induction (Faraday’s Law):

- $ \mathcal{E} = - \frac{d \Phi}{dt} $

- where $ \mathcal{E} $ is the induced electromotive force (EMF), and $ \frac{d \Phi}{dt} $ is the rate of change of magnetic flux.

Importance of Physics Chapter 4 Moving Charges and Magnetism Class 12 Notes

• Foundation for Electromagnetism: This chapter forms the basis for understanding electromagnetism by explaining how electric currents generate magnetic fields and vice versa. It connects key concepts that are fundamental for higher studies in physics and engineering.

• Understanding Magnetic Forces: The notes help in understanding how moving charges interact with magnetic fields, including the forces experienced by charged particles, which is crucial for applications like electric motors and particle accelerators.

• Practical Applications: Knowledge of this chapter is essential for grasping practical applications such as the operation of transformers, electric generators, and magnetic resonance imaging (MRI).

• Problem-Solving Skills: The chapter's notes provide essential formulas and problem-solving techniques for calculating magnetic fields, forces, and currents, which are critical for both board exams and competitive tests.

• Conceptual Clarity: Comprehensive notes offer clear explanations and visual aids that help in grasping complex concepts like Ampere's Law, the Biot-Savart Law, and the motion of charged particles in magnetic fields.

• Exam Preparation: Detailed and well-structured notes are invaluable for revision and preparation, helping students consolidate their understanding and perform better in exams.

Tips for Learning the Class 12 Physics Chapter 4 Moving Charges and Magnetism

1. Understand the Basics: Begin by revising fundamental concepts of Moving Charges and Magnetism. This foundational knowledge will help you grasp how moving charges create magnetic fields.

2. Master Key Formulas: Focus on memorising and understanding the key formulas, such as those for the magnetic field due to a current-carrying conductor, Ampere’s Law, and the force on a moving charge in a magnetic field. Practice applying these formulas in different scenarios.

3. Use Visual Aids: Diagrams and illustrations of magnetic fields, solenoids, and current loops can help visualise complex concepts. Pay attention to how magnetic fields are represented and how they interact with currents.

4. Solve Practice Problems: Work through a variety of problems to apply the theoretical concepts. Practice problems will help reinforce your understanding and improve your problem-solving skills.

5. Relate to Real-Life Applications: Connect theoretical concepts to real-life applications, such as electric motors, transformers, and MRI machines. Understanding how these concepts are used in practical situations can make them more relatable and easier to remember.

6. Review Sample Papers: Go through past exam papers and sample questions to familiarise yourself with the types of questions that may appear. This will help you get comfortable with the exam format and types of problems.

Conclusion

Mastering the concepts of Moving Charges and Magnetism is crucial for building a strong foundation in Physics. The Class 12 notes provided here offer detailed explanations, key formulas, and practical examples to help you understand this essential chapter thoroughly. By regularly reviewing these notes and practising problem-solving, you can enhance your comprehension and perform confidently in your exams. Make the most of these resources to solidify your understanding and excel in your studies.

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