Ncert Exercises & Solutions

Consider a region inside where there are various types of charges but the total charge is zero. At points outside the region:

a.	the electric field is necessarily zero.
b.	the electric field is due to the dipole moment of the charge distribution only.
c.	the dominant electric field is $\propto \frac{1}{r^{3}},$ for large $r$, where $r$ is the distance from the origin in this region.
d.	the work done to move a charged particle along a closed path, away from the region, will be zero.

Which of the above statements are true?
1. (b) and (d)
2. (a) and (c)
3. (b) and (c)
4. (c) and (d)

(4) Hint: Use Gauss law.

Step 1: Interpret the electric field at a large distance.

When there are various types of charges in a region, but the total charge is zero, the region can be supposed to contain a number of electric dipoles. Therefore, at points outside the region (may be anywhere w.r.t. electric dipoles), the dominant electric field

\propto \frac{1}{r^{3}},

for large r.

Step 2: Find the work done in a closed path.

Further, as electric field is conservative, work done to move a charged particle along a closed path away from the region will be zero.

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