Question

(a) If the potential (relative to infinity) is zero at a point, is the electric field necessarily zero at that point? (b) If the electric field is zero at a point, is the potential (relative to infinity) necessarily zero there? Prove your answers, using simple examples.

Short answer

(a) No, the electric field isn't necessarily zero at that point.

(b) No, the electric potential is not necessarily equal to zero.

Step-by-step solution

About Electric field

electric field, an electric property associated with each point in space when charge is present in any form.The magnitude and direction of the electric field are expressed by the value of E, calledelectric field strengthor electric field intensity or simply the electric field.

Determine the electric field

(a) Solution:

No, the electric Field isn't necessarily zero at the point As We know the electric field is a vector filed which is determined by the magnitude and the direction- Also, the electric potential is a scalar which is determined by only the magnitude. So, the electric Field, in this case, is dependent on the direction only. For some direction (contours), the value of the electric field is not equal to zero.

Example:

For this case, the Mo electric charges are equal in magnitude and opposite in sign at the distance 2d. 50, at the midpoint, the electric potential is equal to zero due to the two electric potentials which are equal in magnitude and the opposite direction- Also, at the midpoint, the electric field has a value

Therefore ,No the electric Field isn't necessarily zero at the point

If the electric field is zero at a point, is the potential (relative to infinity) necessarily zero there

(b) Solution:

No, the electric potential is not necessarily equal to zero. As We know the electric ?eld is a conservative ?led- Also, We know

that the electric ?eld is given by the following relation:

By separating the variables and integrating, then the electric potential is equal to constant but it isn't necessarily equal to zero.

Example:

For this case, the two electric charges are equal in magnitude and sign at the distance 2d. 50, at the midpoint, the electric

Field is equal to zero due to the Mo electric Fields are equal in magnitude and opposite direction, So, they cancel each other.

The electric potential has a value at the midpoint

Therefore

(b) No, the electric potential is not necessarily equal to zero.