Question

Electric field due to point charge is E and electric potential V at a distance r from point charge. What will be electric potential for the same point charge at a point where electric field is E/4?

Answer 1

Answer:

Electric potential at that point = V / 2

Explanation:

We know that,

Electric field is the negative potential gradient ie,

Electric field = Potential / Distance

E = V / r

In the first case,

Electric field = E

Potential = V

Distance = r

Hence,

E = V / r

We also know that,

E = kq/r²

r = √(kq / E)

Hence,

E = V / √(kq / E)

In the second case,

Electric field = E/4

Potential = V'

Distance = r'

Hence,

E/4 = V' / r'

We also know that,

E/4 = kq / (r')²

r' = √(4kq / E)

r' = 2 √(kq / E)

Since, r = √(kq / E)

r' = 2r

Putting (r' = 2r) and (E = V / r) in (E/4 = V' / r')

E/4 = V' / r'

V / 4r = V' / 2r

V' = V / 2