Question

The amount of work done to move a positive point charge \(q\) on an equipotential surface of \(1000 \mathrm{~V}\) relative to that done to move the charge on an equipotential surface of \(10 \mathrm{~V}\) is a) the same. b) less. c) more. d) dependent on the distance the charge moves.

Short answer

Question: Compare the work done to move a positive point charge q on two different equipotential surfaces, one with a voltage of 1000 V and the other with a voltage of 10 V. Is the work done: a) the same b) greater on the 1000 V surface c) greater on the 10 V surface Answer: a) the same

Step-by-step solution

Define the work done on an equipotential surface

Equipotential surfaces are surfaces where the electric potential is constant. This means that the electrical potential energy of the charge remains the same as it moves along the surface. Therefore, there is no change in electrical potential energy, and consequently, no work is done in moving the charge along an equipotential surface.

Relate work done to the potential difference

To compare the amount of work done to move the positive charge q on the two equipotential surfaces (1000 V and 10 V), we need to relate work to the potential difference. The work done in moving a charge q from one point to another in an electric field is given by the equation: W = q * (V_final - V_initial).

Compare the work done in both cases

Since we are moving the charge along an equipotential surface (with constant potential), the potential difference (V_final - V_initial) is zero for both cases. Therefore, using the equation from Step 2, the work done in both cases is: W = q * 0 = 0. Since the work done in both cases is the same (zero), the correct answer is: a) the same.