Electric Charges and Fields

Step 1: Analyze the configuration \((A)\).
This configuration is analogous to two bar magnets on a straight line, with the north poles of both magnets facing right. In this case, the magnets will attract each other.
 

Step 2: Analyze the configuration \((B)\).
This configuration is analogous to two bar magnets on a straight line, with the north poles of both magnets aligned in opposite directions, as shown in the figure. In this case, the magnets will repel each other.
 
Hence, option (1) is the correct answer.
 

Step: Find the ratio of \(\frac{\phi_0}{V_0}\).
The electric flux due to charges from the outer surface of the sphere is given by; 
\(\phi_0 = \frac{q_1+q_2}{\varepsilon_0}~~~…(1)\)
The potential due to a spherical conducting shell is given by; 
\(V_0 = \frac{1}{4\pi \varepsilon_0} \frac{q_1+q_2}{R}~~~…(2)\)
From the equations \((1)\) and \((2)\) we get; 
The ratio of \(\frac{\phi_0}{V_0}\) is \(\frac{\frac{q_1+q_2}{\varepsilon_0}}{\frac{q_1+q_2}{4\pi \varepsilon_0 R}}= \frac{4\pi \varepsilon_0 R}{\varepsilon_0}= 4\pi R\)
Therefore, the ratio \(\frac{\phi_0}{V_0}\) is proportional to \(R.\)
Hence, option (2) is the correct answer.