Q. 65

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?

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=VB-VA=VB-0=VB

Here VB is the potential at general point (x,y,z) and VA 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, VB 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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Superfast Revision of Potential & Potenial Energy (Theory + Interactive Quiz)47 mins
Check your knowledge of Electric Potential | Quiz45 mins
Relation between electric field and potential34 mins
Relation between Electric field & Potential45 mins
Interactive quiz on Relation between electric field and potential43 mins
Electric field inside cavity37 mins
Few Applications of Gauss's law54 mins
Electric potential inside solid and hollow sphere30 mins
Test Your Knowledge of Electric Charge & Coulomb's Law47 mins
Electric Field Lecture47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses