Question

The electric field at a point in space is a measure of

(a) The total charge on an object at that point.
(b) The electric force on any charged object at that point.
(c) The charge-to-mass ratio of an object at that point.
(d) The electric force per unit mass on a point charge at that point.
(e) The electric force per unit charge on a point charge at that point.

Answer 1

The coulomb’s law states that the electrostatic force between two-point charges is directly proportional to the product of these two charges. The force is inversely proportional to the square of the distance between these charges.

 

The expression of the coulomb’s force is,

F = kq1q2/r2

 

Here, F is the Coulomb’s force, k is the coulomb’s law, r is the distance, q1 and q2 are the charges.

 

The expression of the electric force in terms of electric field is,

F = qE

 

Here, F is the electric force, q is the charge, and E is the electric field.

 

The charge to mass ratio is,

e/m = υ/rB

 

Here, e is charge on electron, m is mass, v is velocity, r is distance, and B is magnetic field.

 

The acceleration in terms of force and mass on an object according to Newton’s second law is,

a = F/m

 

Here, a is acceleration, F is force, and m is mass.

 

Rearrange equation F = qE for E.

E = F/q

 

Consider that the charge is q for both point-charges. The expression of the coulomb’s force is,

F = kqq/r2

 

Substitute kqq/r2 for F.

E = 1/q(kqq/r2)

E = kq/r2

 

The electric field is directly proportional to the point-charge and inversely proportional to square of distance.

 

The electric field depends on the point charge but is not a measure of the total charge on an object where electric field is to be determined.

 

The electric field is force per unit charge so, electric force is not equal to electric field.

 

The charge to mass ratio depends on the velocity of the charge, radius, and the magnetic field i.e. (e/m = v/rB). so, it is not equal to electric field.

 

The force per unit mass is equivalent to acceleration. Thus, this also does not define electric field.

 

The electric field in terms of electric force and charge is,

E = F/q

 

The electric field is defined as the electric force per unit charge at that point.

Therefore, the correct option is (e).

The correct option is (e).