Basic Idea about Magnetic Field
In this article, you will learn the behavior of the forces performing on a dipole in a uniform magnetic field and will correlate it with the situation when a dipole is retained in an electrostatic field. For example, we experience that if we keep the iron fillings near a bar magnet upon a piece of paper and pound the sheet, the fillings assemble themselves to create a particular design. Here, the arrangement of iron filings signifies the magnetic field lines produced by the magnet. These lines generated due to the magnetic field provide us a fairly accurate clue of the magnetic field. On the other hand, most often, we are prescribed to govern the amount of magnetic field B precisely. We achieve this by employing a small compass needle of identified magnetic moment (m) and moment of inertia and let it oscillate in that particular magnetic field.
The region around a magnet within which another magnet can influence is called the Magnetic Field . A series of lines around a magnet is represented as a magnetic field. The magnetic field is one of the most important topics of physics.
Apart from the book, we also use a magnetic field in our daily life. Let us get familiar with the term and enjoy the study of Vedantu. Students are going to have fun when they know about the uses. Here are some uses like
Computer hard disk
Television
Radio
Telephone
Microwaves oven.
A pair of two equal and opposite forces having a different line of action gives rise to a turning effect known as torque along the axis, which is perpendicular to the plane of the force.
Students can describe the magnetic influence on moving electric charges; electric currents and magnetic materials are magnetic fields. It is a vector field. A moving charge present in a magnetic field experiences a force perpendicular to its velocity and the magnetic field.
A magnetic field permanent magnets pull on ferromagnetic materials such as iron and attract or repel other magnets. Also, a magnetic field that varies with location will exert a force on a range in respect to non-magnetic materials by affecting the motion of their outer atomic electrons. Those Magnetic fields surrounding magnetized materials are created by electric currents such as those used in electromagnets and electric fields may vary in time.
The strength and direction of a magnetic field may sometimes vary with location; it is described by a function assigning a vector mathematically to each point of space, called a vector field.
Torque on a Magnetic Dipole in a Uniform Magnetic Field
Usually, a Magnetic dipole is a small magnet of atomic to subatomic sizes, similar to a flow of electric charge around a loop. Electrons rotating on their axes, electrons passing around atomic nuclei, and spinning positively charged atomic nuclei all are magnetic dipoles.
The addition of these effects may cancel so that a specified type of atom may not be a magnetic dipole. If they do not fully cancel, the atom is an everlasting magnetic dipole. Such dipoles are iron atoms. Millions of iron atoms locked with the same arrangement spontaneously creating a ferromagnetic domain also create a magnetic dipole.
Magnetic compass needles, and magnetic bars are examples of macroscopic magnetic dipoles.
Let’s take a magnet bar (N-S) having the length 2l and the pole strength m located in a uniform magnetic field of induction denoted as B by creating an angle θ with the field direction, as shown in the figure below. Because of this magnetic field denoted by B, the first force (m ∗ B) executes on the North Pole along the magnetic field direction, and another force (m ∗ B) executes on the South Pole along the opposite direction to the magnetic field. These two new forces are identical and inverse,
Therefore it establishes a couple.
Torque on a Magnetic Dipole in a Uniform Field
When a magnetic rod, (which can be taken as a magnetic dipole), is kept in a uniform magnetic field, the North Pole senses a force equal to the multiplication of the magnetic field intensity and the pole strength in the magnetic field direction.
Nonetheless, the South Pole senses a force, equal in magnitude but opposite in direction. Hence a torque exerts on the magnetic dipole because of which the magnet starts to rotate.
The torque is denoted as τ because the couple is:
τ = Force ∗ Perpendicular distance
= F ∗ NA------(1)
We know, F = m ∗ B
So, = mB ∗ 2l sin θ
= MB sin θ------(2)
It can be written in the vector form
as τ = \[M^{\rightarrow}* B^{\rightarrow}\]
We also know that the direction of τ is perpendicular to the plane and;
If θ = \[90^{0}\] and B = 1
Then we can obtain from equation (2), τ = M
Thus, the torque, which is essential to keep the magnet at \[90^{0}\] with a magnetic field, is equal to the magnetic moment induction.
Electrostatic Analog
Let's compare the equation of electric dipole in an electric field. We conclude that the magnetic field due to a bar magnet at a considerable distance is analogous to an electric dipole in an electric field. Likewise, the relation can be status as given below,
E→B,p→m,\[\frac{1}{4\pi\varepsilon_{0}}\rightarrow \mu_{0}4\pi E\rightarrow B\], ,p→m,\[\frac{1}{4\pi\varepsilon_{0}}\rightarrow \mu_{0}4\pi\]
If the value of r, that is, the distance of the point from the given magnet, is tremendous as compared to the size of the magnet given by I, or r >> l, then students can write the equatorial field generated by a bar magnet as,
BE=−\[\frac{\mu_{0}m}{4\pi r}\]
3BE=−\[\frac{\mu_{0}m}{4\pi r^{3}}\]
Comparably, the axial field of the bar magnet in the same condition can be given as,
BA=−\[\frac{\mu_{0}2m}{4\pi r}\]
3BA=−\[\frac{\mu_{0}2m}{4\pi r^{3}}\]
Stay updated with Vedantu to learn more about dipoles in a uniform magnetic field, the electrostatic analog, and other related topics.
FAQs on Dipole Uniform Magnetic Field
1. A Bar Magnet Having Moment 0.31 JT⁻¹ is Kept in a Uniform External Magnetic Field of 0.14 T. If the bar is Allowed to Rotate in the Plane of the Field, Which Coordination Would Agree to its (a) Stable (b) Unstable Equilibrium? Find the Potential Energy of the Magnet in Both Cases?
Given M = 0.31 JT⁻¹
B = 0.14 T
Θ = Angle between the bar magnet and the magnetic field
In stable equilibrium, Θ = 0⁰
P.E= - M ∗ B Cos Θ = - 0.31∗ 0.14 ∗ Cos 0⁰ = - 4.3 ∗ 10⁻² J
In unstable equilibrium, Θ = 180⁰
P.E=- M ∗ B Cos 180 = - 0.31∗ 0.14 ∗ Cos 180⁰ = 4.3 ∗ 10⁻² J
2. Explain about EMF and Give its Formula?
EMF is known as Motional Electromotive Force. An EMF persuaded by the motion of the conductor through the magnetic field is a motional electromotive force.
The equation is given by E = -v ∗ L ∗ B.
3. Is Electric Dipole Moment Scalar or Vector?
It is a vector quantity. The charge direction is from the negative to the positive.
In vector form, it is written as:
p = q→ ∗ d→
4. What is the Dipole Moment? Give an Example?
Polar molecules show a huge difference in the electrical charge at the positive end, as well as at the negative end. Alternatively, it is known as a dipole moment.
For illustration, ammonia (NH₃) is a polar molecule. This NH₃ contains one nitrogen atom covalently bonded to three hydrogen atoms as a result of the dipole moment.
5. What is the magnetic dipole moment, and how is it related to torque?
As the coil turns, the direction of the magnetic field also turns with the coil. Suppose the magnetic field is not changing, then the torque will help create in the reverse direction by the rotation of the magnetic moment. So from this, the student can understand that the torque causes the loop to accelerate in the opposite direction. Torque and magnetic field both are vectors, and the torque created is related to the orientation of the loop.
6. Why does one care about the magnetic dipole moment?
The electron and proton both have a magnetic dipole moment. The total magnetic moment of a magnet tells us about the rotation torque. A magnetic moment is the critical feature of tactic magnetism found in nature. The difference in the magnetic moment of protons in the human body and the basis of MRI imaging and also NMR for chemistry.
7. What is the meaning of 'moment' in the magnetic moment and Dipole?
Dipole moment is the leading property of Dipole that decides the strength and also the direction of the field everywhere. Also, The same holds true for a magnetic dipole. Magnetic Dipole is significant because Dipole is found everywhere in nature. For example, one can say that water molecules are electric dipoles and magnets have magnetic dipoles inside them
8. Are the magnetic moment and magnetic Dipole moment different?
No, magnetic moment and magnetic dipole moment are the same. The strength of a magnetic dipole is known as the magnetic dipole moment. Definition of both magnetic moment and magnetic dipole moment contains the same quantity. A magnetic dipole arises due to the current loop. After that magnetic dipole moment is calculated by multiplying the area with the current. The direction must always be perpendicular to the surface. It can be calculated using the corkscrew rule.
9.How does Vedantu give you helpful information about the Dipole Uniform Magnetic Field?
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