Step 1: The potential at the surface of a uniformly charged spherical shell is the same as the potential at any point inside the shell (including the center). This result holds for spherical symmetry in electrostatics.
Step 2: Thus, the potential at the center of the shell is the same as the potential on the surface of the shell. Since the surface potential is 60 V, the potential at the center is also 60 V.
Match List - I with List - II:
List - I:
(A) Electric field inside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \).
(B) Electric field at distance \( r > 0 \) from a uniformly charged infinite plane sheet with surface charge density \( \sigma \).
(C) Electric field outside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \).
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density \( \sigma \).
List - II:
(I) \( \frac{\sigma}{\epsilon_0} \)
(II) \( \frac{\sigma}{2\epsilon_0} \)
(III) 0
(IV) \( \frac{\sigma}{\epsilon_0 r^2} \) Choose the correct answer from the options given below:
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively: