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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