Question

3. a) A positive 20µC charge is placed at the centre of a circle of radius 20 cm. If we
move a positive 2µC charge once along the circumference of the circle, will any
work be done in the process? Justify your answer.

Answer 1

Answer on Question #79543 - Physics - Electric Circuits

3. a) A positive $20\mu \mathrm{C}$ charge is placed at the centre of a circle of radius $20~\mathrm{cm}$. If we move a positive $2\mu \mathrm{C}$ charge once along the circumference of the circle, will any work be done in the process? Justify your answer.

Solution

Calculate the electric potential done by $Q = 20 \mu \mathrm{C}$ charge at a distance $r = 20 \, \mathrm{cm}$ in any direction:

$$V _ {1} = \frac {Q}{4 \pi \varepsilon_ {0} r} = \frac {2 0 \cdot 1 0 ^ {- 6}}{4 \cdot 3 . 1 4 \cdot 8 . 8 5 \cdot 1 0 ^ {- 1 2} \cdot 0 . 2} = 8. 9 9 \mathrm {M V}.$$

If the smaller charge is moved once along the circumference, it will constantly be at a distance $20\mathrm{cm}$ from the first charge where potential $V$ is also equal to $V_{1}$. And the work done on the charge $q = 2\mu C$ is:

$$W = q \left(V _ {1} - V\right) = 2 \cdot 1 0 ^ {- 6} \left(8. 9 9 \cdot 1 0 ^ {6} - 8. 9 9 \cdot 1 0 ^ {6}\right) = 0.$$

Thus, no work will be done in this process; the $2\mu \mathrm{C}$ charge is moving along the equipotential lines.

Answer

No work will be done because the smaller charge moves along the equipotential lines.

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