1. Is there any limit in the lowest amount of charge on a body?

Yes. A body becomes charged when the body gains or loses some extra electrons. So, the minimum number of the electrons, a body can gain or lose must be one. As the amount of charge on an electron is fixed at , the same can be the minimum positive or negative charge on a body.

2. Two hollow conductors contain positive charges. The smaller one is at and the bigger one is at . How should you arrange them so that the positive charges flow from the smaller to the bigger conductor when a wire connects them?

We place the smaller conductor within the bigger one. As a result, the charges will flow in the outward direction. Because the charges always remain on the outer surface of a conductor. Here, the two body forms a single conductor when connected.

3. What can you comment about the electric field () in a region of space where the electric potential () is uniform throughout?

In a space with uniform potential everywhere, the electric field .

This results from the relation

or from the definition of electric field. In presence of an electric field, work is to be done to shift a test (unit positive) charge opposite to the direction of the field. This work done, in this case, measures the difference in potential between the points. The potential difference between any two points in a space of uniform potential is zero. So, this work done is zero as well. But the distance between the two points () cannot be zero. Hence, here, .

4. What can you comment about the electric potential () in a region of space where the electric field () is uniform throughout?

The direction of electric field is perpendicular to an equipotential surface. In this case, the electric field is uniform. Hence, the equipotential surfaces are plane surfaces with decreasing value along the direction of the electric field.

5. A charge of 5 C is placed at the center of a hollow metallic conductor. Its inner and outer radii are 20 cm and 40 cm, respectively. Determine the electric field at (a) 10 cm, (b) 30 cm, and (c) 50 cm from the center. [For a complete explanation of this type of problems on Gauss’ law watch this video]

The answer for (b) can be given readily. The given point is at 30 cm from the center. Hence this point is inside a metallic conductor. As a result the electric field is zero as this point.

We can solve these problems using concentric spherical Gaussian surfaces of radii (a) , (b) , and (c) . Induced charges are generated at the inner and outer surfaces ( -5C and +5C, respectively).

Therefore, following Gauss’ law:

the electric fields are:

(a) , and hence .

(b) , and hence .

(c) , and hence .

Here, is the amount of charge that the Gaussian surface encloses. The direction of electric fields are perpendicular to the surfaces (and outward, as the charge is positive).

6. A charged particle is seen to be moving in an electric field along a straight line. What can you comment about the motion of the particle?

A charged particle must experience a force in an electric field resulting in change in its velocity. As the particle is not changing its direction it must change the magnitude of its velocity. Therefore we can say the charge particle moves with an acceleration or retardation.