A charge \( -6 \, \mu C \) is placed at the center B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge \( +5 \, \mu C \) is moved from point C to point A along the circumference. Calculate the work done on the charge.
Show Hint
The work done in moving a charge in an electric field depends on the potential difference between the initial and final points. If the potential is the same, no work is done.
The work done in moving a charge in an electric field is given by:
\[
W = q \Delta V
\]
where \( \Delta V \) is the potential difference between the points A and C, and \( q \) is the charge being moved.
The potential at a point due to a charge is given by:
\[
V = \frac{kQ}{r}
\]
where \( Q \) is the charge and \( r \) is the distance from the charge. Since the charge is moving along the semicircle, the potential difference between points A and C is the same due to the symmetry of the setup. Since the charges at B and D are equal and opposite, they cancel out in terms of potential at the points along the semicircle.
Thus, the work done on the charge when moving from C to A is zero because the potential at points A and C is the same.
Hence, the work done on the charge is \( \boxed{0} \).
