Electric Field Intensity

An electric field is defined as the space around a charge or charged body in which other charges (less in magnitude than source charge) experience an electric force. It can be further defined as the force experienced per unit test charge.

The Electric field intensities are important in many areas of physics and are exploited practically in electrical technology as well. Taking an atomic scale, we can define that the electric field is responsible for the attractive force between the atomic nucleus and electrons that hold atoms together and the forces between atoms that cause chemical bonding.

The subatomic particles in an atom, such as electrons and photons, carry an electric charge. An electron has a charge of roughly 1.602×10-19 coulombs. Every charged particle produces a space in which the impact of its electric force can be felt. 

When a unit test charge is placed in this electric field, it will experience a force. The amount of force experienced by the unit charge is known as the electric field intensity.

Electric Field Intensity Formula

An electric field's intensity is a vector quantity. It has a magnitude as well as a direction. Even if the test charge is at rest, it will experience force when it is exposed to the source charge's electric field.

Consider a charged particle ‘Q'. An electric field surrounds this charged particle. This charged particle is referred to as a source charge since it is the source of the electric field. 

By inserting another charge in the source charge's electric field, the strength of the source charge's electric field can be calculated.

This external charge particle is called the test charge because it is used to measure the electric field strength. Let 'q' be the charge on the test charge.

An electric force or force that repels will happen when a test charge is in the electric field.

Let's call it 'F' for force. " The force per charge on the test charge" can now be used to describe the magnitude of the electric field strength. As a result, the intensity of the electric field 'E' is given as

                                           E = F/q          (Equation1)

The charge on the test particle is taken into account rather than the source charge. In SI units, electric field intensity is measured in Newton per coulombs.

The intensity of the electric field is independent of the particle's charge. It is measured around the source charge regardless of the test charge particle's charge.

The mass and velocity of the test charge particle have no effect on the electric field strength.

The amount of charge on the test charge particle is all that matters.

A positively charged particle or a negatively charged particle might be used as the test charge.

The charge on the test charge particle determines the direction of the electric field. 

The test charge is assumed to be a positive charge when determining the direction of electric field intensity.

So, when a positive test charge particle enters this electric field, it is repelled.

So the electric field strength will be directed away from the charge. However, the direction of force for electric field strength for a negatively charged test charge will be towards the source charge particle.

Electric Field Intensity due to the System of Discrete Charges

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The electric field intensity due to the system of discrete point charges is obtained by vector addition of intensity due to the number of charges q1, q2,………....., qn. The resultant electric field intensity at that point due to these charges is given by the superposition theorem.

Electric Field Intensity due to the Uniform Charge Distribution

For finding electric fields due to continuous charge distribution, we consider the term charge density as a measure of electric charge per unit length for linear distribution, the charge per unit area for areal distribution and charge per unit volume for volumetric distribution. A surface charge density σ at an area element is given by

The linear charge density λ of a wire is defined by λ = ΔQ/Δl, where λ is the linear charge density, Δl is a small line element of wire and ΔQ is the charge in that elemental portion

The areal charge density for a sheet of charge is given by σ = ΔQ/ΔA

Where

ΔQ is the charge and ΔA is the area element.

The volume charge density is defined by 

ρ = ΔQ/ΔV

Where ΔV is volume element and ρ is volume charge density.

Strength of Electric Field

The electric field is a function of vector position. Electric field intensity at any point in the electric field is defined as the force experienced by unit test charge at that point.

E = F/q = Force (Electrostatic force experienced per unit test charge)

Here F = kqQ/r²

Thus, E = kQ/r²

We can see that the electric charge is independent of the test charge that is placed to determine the field thus is totally characteristic of the system of charges.

Here, q is the test charge and Q is the charge due to which field is to be found out.

Thus, the S.I. unit of the electric field is NC⁻¹.

Electric Field Intensity Direction

Electric Field Intensity due to a Point Charge

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Electric field intensity due to a positive point charge is directed towards it while due to negative point charge, it is directed away from it.

Properties of Electric Field

• The electric field does not depend upon the test charge.

• Electric charge is along the direction in which the test charge would tend to move.

• If the source charge is positive, the direction of the electric field is along the direction of electric force.

• If the source charge is negative the direction of the electric field is opposite to the direction of electric force.

• If the source charge is greater than zero, the field is radially outwards.

• If the source charge is less than zero, the field is radially inwards.

• If Identical charges are placed on each vertex of a regular polygon then the electric field at the centre is Zero.

Force Experienced by a Charge in an Electric Field

The electrostatic force experienced by a charge of magnitude q placed in an electric field of strength E is given by:

If q is positive, the force acts in the direction of E and equals to F=qE

If q is negative, the force acts in the direction opposite to E and is given by F=qE 

This force is experienced on a charge placed in an electric field whether it is at rest or motion and this force is independent of mass as well as the velocity of the charged particle. The force experienced by a proton and an electron in the same electric field is equal in magnitude and opposite in direction.

Also, if the charge has some initial velocity, the force on the proton is accelerating in nature while that on the electron is retarding force.

The ratio of acceleration of proton/Retardation of electron = mass of an electron/mass of a proton.

Electric Lines of Force

Electric lines of force are imaginary lines which are continuous straight or curved, tangent to a point on the line, giving the direction of electric field vector and number of lines per unit area that is the density of lines is proportional to the magnitude of E.

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The exact strength of the electric field is measured by the total number of lines passing per unit area of the surface which is passing perpendicular to the surface.

Properties of Electric Lines of Force

• Electric lines of force start from the positive charge and end at the negative charge.

• Number of electric lines of force start or end on the charge is proportional to their magnitude

• Electric lines of force do not form a closed loop.

• Electric lines of force do not cross each other.

• Electric lines of force are always perpendicular to the conducting surface.