1

Given is a line of charge of uniform linear density. A charge +q is distributed uniformly between y = 0 and y = a and charge –q is distributed uniformly between y = 0 and y = -a.

Explain how the direction of the resultant electric field at point P can be obtained. Represent using a vector diagram.

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Solution

The x-components of E1 and E2, due to two equidistant points on either side of O, cancel each other. The resultant electric field is due to the superposition of the y-components of E1 and E2. The direction of the net electric field is along the negative y-axis. This is true for all pairs of equidistant points on either side of O.

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2

A charge of 10 C each is given to two spherical conductors A and B. The volumes of A and B are in ratio of 1:3. When A and B are connected by a conducting wire, show that it is impossible for the charge to flow from

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Solution

Potential on the surface of spherical conductor = [1 mark for the correct formula of potential in terms of the radius of conductor] The greater volume of sphere B corresponds to a greater radius RB. RA < RB . So for the same charge given to the two spherical conductors, the conductor with a smaller radius, that is, B is at the lower potential. VA > VB The charge always flows from a body at a higher potential to a body at a lower potential. Hence, it is impossible for the charge to flow from B to A as VB < VA.

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