Question

6. 2075 Set A Q.No. 46) Is it possible that electric potential at a
point is zero but not electric field?
[2]​

Answer 1

Answer:

1. (a) No, just because the electric field is zero at a particular point, it does not necessarily

mean that the electric potential is zero at that point. A good example is the case of two

identical charges, separated by some distance. At the midpoint between the charges, the

electric field due to the charges is zero, but the electric potential due to the charges at that

same point is non-zero. The potential either has two positive contributions, if the charges

are positive, or two negative contributions, if the charges are negative. (b) No, just

because the electric potential is zero at a particular point, it does not necessarily mean

that the electric field is zero at that point. A good example is the case of a dipole, which

is two charges of the same magnitude, but opposite sign, separated by some distance. At

the midpoint between the charges, the electric potential due to the charges is zero, but the

electric field due to the charges at that same point is non-zero. Both the electric field

vectors will point in the direction of the negative charge.

3. (a) Zero. The potential at infinity is zero, and the potential at the midpoint of the

dipole, due to the charges on the dipole, is also zero. The potential difference is zero, so

no net work is done. (b) Still zero. The path followed does not matter because the electric

force is conservative – all that matters is the potential difference between the initial point

and the final point, which is zero.

5. 1 is not possible – field lines and equipotentials are perpendicular to one another where

they cross. 2 is not possible – for one thing, equipotentials can not cross one another. 3

looks fine – it looks pretty close to a dipole situation.

7. (a) +4q (b) –6q (c) +4q

9.

Potential

difference

Capacitance Charge Field Energy

Initially V0 C0 Q0 E0 U0

Dielectric

removed

V0 C0 /3 Q0 /3 E0 U0 /3

Distance

halved

V0 2C0 /3 2Q0 /3 2E0 2U0 /3

11. (a) The capacitor does work on the dielectric, attracting it inside the capacitor.

(b) You do work on the dielectric to bring it back out of the capacitor.

13. 3.1 × 106

m/s

15. 7.5 m/s

17. (a)

2 6kq

r − (b)

2 12kq

r − (c)

2