61.
Charges $$+q$$ and $$-q$$ are placed at points $$A$$ and $$B$$ respectively which are a distance $$2L$$ apart, $$C$$ is the midpoint between $$A$$ and $$B.$$ The work done in moving a charge $$+Q$$ along the semicircle $$CRD$$ is
A
$$\frac{{qQ}}{{2\pi {\varepsilon _0}L}}$$
B
$$\frac{{qQ}}{{3\pi {\varepsilon _0}L}}$$
C
$$ - \frac{{qQ}}{{6\pi {\varepsilon _0}L}}$$
D
$$\frac{{qQ}}{{4\pi {\varepsilon _0}L}}$$
Answer :
$$ - \frac{{qQ}}{{6\pi {\varepsilon _0}L}}$$
62. Two concentric spheres of radii $$R$$ and $$r$$ have similar charges with equal surface charge densities $$\left( \sigma \right).$$ What is the electric potential at their common centre ?
A
$$\frac{\sigma }{{{\varepsilon _0}}}$$
B
$$\frac{\sigma }{{{\varepsilon _0}}}\left( {R - r} \right)$$
C
$$\frac{\sigma }{{{\varepsilon _0}}}\left( {R + r} \right)$$
D
None of these
Answer :
$$\frac{\sigma }{{{\varepsilon _0}}}\left( {R + r} \right)$$
63. Two conducting spheres of radii $${R_1}$$ and $${R_2}$$ having charges $${Q_1}$$ and $${Q_2}$$ respectively are connected to each other. There is
A
no change in the energy of the system
B
an increase in the energy of the system
C
always a decrease in the energy of the system
D
a decrease in the energy of the system unless $${Q_1}{R_2} = {Q_2}{R_1}$$
Answer :
a decrease in the energy of the system unless $${Q_1}{R_2} = {Q_2}{R_1}$$