A uniform field of 2.0 NC –1 exists in space in x-direction. (a) Taking the potential at the origin to be zero, write an expression for the potential at a general point (x, y, z). (b) At which points, the potential is 25 V? (c) If the potential at the origin is taken to be 100 V, what will be the expression for the potential at ta general point? (d) What will be the potential at the origin if the potential at infinity is taken to be zero? Is it practical to choose the potential at infinity to be zero?

Question

Philoid · Accepted Answer

Given:
(a)Magnitude of Electric field: E = 2.0 NC^–1
V(0,0,0) = 0 V
(b) V= 25 V
(c) V(0,0,0) = 100 V
Formula used:
(a) Electric field exists in x-direction.
We know that, Potential difference is :

V=V_B-V_A=V_B-0=V_B
Here V_B is the potential at general point (x,y,z) and V_A is the potential at origin = 0.
Potential is given a
V = -E.r
Where E is the electric field and r is the position of the point in space.
In vector form:

Substituting ,

Here, y and z components are not considered as electric field is along x direction.
Hence expression of potential at a general point (x,y,z) in space is -2x V.
(b)
Here, V_B is 25 V.

Hence at x= -12.5 m, potential is 25 V.
(c)
Now similar to part (a), here potential at origin is given and we need to find potential at general point.
V(0,0,0) = 100 V
Using formula for potential derived in (a) we get,

Let potential at infinity be : V_∞ = 0 and x=∞
Potential at origin is : V₀
Using the formula for potential and result of (a):

Hence, potential at origin is infinite.
It is not practical to choose potential at infinity to be zero as it will make potential at origin to be infinite as we derived which will make the calculations impossible.