# Electric Field-

Electric field due to an Electric Charge can be defined as-

 The region or space around an electric charge in which any other charge experiences an Electric Force is called as electric field. OR The region or space around an electric charge within which its influence can be felt by any other charge is called as electric field.

• The charge which produces the electric field is called as a source charge.
• The charge which tests the effect of source charge is called as a test charge.

## Electric Field Intensity-

 The electric field intensity at any point is the strength of electric field at that point. It is defined as the force experienced by a unit positive charge placed at that point.

If F is the force acting on a small test charge q0 at any point, then electric field intensity at this point is given by-

(Equation-01)

Since the charge q0 may disturb the electric field of the source charge, so the test charge q0 must be small enough.

It is better to define electric field intensity at a point as the force per unit test charge acting on a vanishingly small positive test charge placed at that point.

Hence,

It is important to note that the term electric field intensity is interchangeably used with the term electric field.

### Direction of Electric Field-

We have-

(From Equation-01)

The direction of electric field is same as the direction in which the test charge tends to experience the force.

#### Always Remember

The direction of electric field at any point is always along the line joining the source charge and the observation point.

• If the source charge is positive, the direction is away from the source charge.
• If the source charge is negative, the direction is towards the source charge.

### Unit of Electric Field-

As the electric field is force per unit charge, so its SI unit is newton per coulomb (NC-1).

### Dimensional Formula of Electric Field-

As the electric field is force per unit charge, so its dimensional formula can be derived as-

### Force on Charge In An Electric Field-

We know, if F is the force acting on a small test charge q0 at any point, then electric field intensity at this point is given by-

(From Equation-01)

From here, the force F on a charge q in a uniform electric field having electric field intensity E is given by-

(Equation-02)

#### Important Notes

• A positively charged particle always experiences a force in the direction of electric field.
• A negatively charged particle always experiences a force in the direction opposite to that of electric field.

### Acceleration of Charge In An Electric Field-

We know, the force F on a charge q in a uniform electric field having electric field intensity E is given by-

(From Equation-02)

#### Important Notes

• The acceleration of a particle in an electric field depends upon its charge as well as its mass.
• A positively charged particle always accelerates in the direction of electric field.
• A negatively charged particle always accelerates in the direction opposite to that of electric field.

### Electric Field Intensity Due To A Point Charge-

Consider a source point charge Q placed at point O. We wish to calculate the electric field intensity at point P located at distance r from it.

We place a small test charge q0 at point P as shown-

By Coulomb’s law, the magnitude of force experienced by the test charge q0 is given by-

The magnitude of electric field intensity at point P is given by-

Substituting the value of F, we get-

On solving, we get-

• We use the above formula for finding the magnitude of electric field intensity due to a point charge at a distance r from it.
• The direction of electric field is same as the direction in which the test charge tends to experience the force.

### Graph-

The following graph shows the variation of electric field intensity due to a point charge with distance from it-
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