NEET Physics Notes Electrostatics-Electric Field

NEET Physics Notes Electrostatics-Electric Field

Electric Field

Electric Field

The space surrounding an electric charge q in which another charge q0 experiences a force of attraction or repulsion, is called the electric field of charge q. The charge q is called the source charge and the charge q0 is called the test charge. The test charge must be negligibly small, so that it does not modify the electric field of the source charge.
Electric field vector E (also known as the electric field intensity) at any point, is given by

where, q0 is a small positive test charge which experiences a force F at a given point.
SI unit of electric field is NC-1 and it is also known as Vm”1. The dimensional formula for electric field is [MLT^A-1].

Electric Field Lines

An electric field line in an electric field is a smooth curve, tangent to which, at any point, gives the direction of the electric field at that point.

Motion of a Charged Particle in an Electric Field

A charged particle is released from rest in an electric field E.
Then, force on charged particle is given by
F=qE
The acceleration produced by this force is given

Since, E is constant, the acceleration a is also constant. Hence, the particle is uniformly accelerated. Let the particle starts from rest, then given by v = u + at

The distance travelled by the particle is given by

The kinetic energy gained by the particle

A charged particle enters the field in perpendicular direction.
Let a charged particle of mass m and charge charge q, enters the electric field along X-axis with speed u. The electric field E is along Y-axis is given by F_y = qE
and force along X-axis remains zero, i.e. F_x = 0

Acceleration of the particle along Y-axis is given by

The initial velocity is zero along Y-axis ( U_y = 0).
The deflection of charged particle along Y-axis after time t is given by

Along X-axis there is no acceleration, so the distance covered by particle in time t along X-axis is given by x = u_t Eliminating t, we have

This shows that the path of charged particle in perpendicular field is a parabola.

Important properties of electric field lines are

• Electric field lines come out of a positive charge and go into the negative charge.
•  No two electric field lines intersect each other.
•  Electric field lines are continuous but they never form a closed loop.
•  Electric field lines cannot exist inside a conductor. Electric shielding is based on this property.

Electric Field due to a Point Charge

Electric Field at a Distance r from a Point Charge q is

If ql and are two like point charges, separated by a distance r, a neutral point between them is obtained at a point distant r₁ from q_v such that

If q₁ and q₂ are two charges of opposite nature separated by a distance r, a neutral point is obtained in the extended line joining them, at a distance  r₁ from q_v such that

Electric Field due to Infinitely Long Uniformly Charged Straight Wire

Electric field at a point situated at a normal distance r, from an infinitely long uniformly charged straight
wire having a linear charge density λis given by

Electric Field due to a Charged Cylinder

For a conducting charged cylinder of linear charge density λ and radius R, the electric field is given by

Electric Field due to a Uniformly Charged Infinite Plane Sheet

Electric field near a uniformly charged infinite plane sheet having surface charge density σ is given by

Electric Field due to a Uniformly Charged Thin Spherical Shell

For a charged conducting sphere/ shell of radius R and total charge Q, the electric field is given by

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