Quiz 6 (PHYS262, Summer 2001)

August 22, 2001

1)

A spherical conducting shell has a radius of $R$ and charge of $Q$. A point $P$ is located inside the shell at a distance $r$ from the centre of the sphere, where $r<R$. What is the electric potential at point $P$?

(a) $0$ (b) ${1\over 4\pi\epsilon_0}{Q\over r}$ (c) ${1\over 4\pi\epsilon_0}{Q\over R}$ (d) ${1\over 4\pi\epsilon_0}({Q\over r}-{Q\over R})$ (e) Not enough information

2)

In a certain spherically symmetric system, the electric potential $V$ as a function of the distance $r$ from the centre is shown in Fig. 1. Which of the following statements is FALSE?

(a) The electric field is positive (in the radial direction) between $r=r_0$ and $r=r_1$.

(b) A particle with a positive charge $q$ which has a kinetic energy of $K$ larger than $qV_0$ at $r=0$ will have a kinetic energy of $K-qV_0$ at $r=r_0$.

(c) The electric field is zero at $r=r_0$ and $r=r_1$.

(d) A particle with a negative charge located at $r>r_1$ will be accelerated towards the centre ($r=0$).

(e) None of the above.

3)

Figure 2 shows a voltage-charge ($V$-$Q$) diagram of the process of charging a certain capacitor, from the point $O$ to the point $P$. What is the total work required for this process? One unit of voltage and charge is $V_0$ and $q_0$ respectively in the graph.

Figure 1: Prob 2

Figure 2: Prob 3

(a) $12V_0q_0$ (b) $6V_0q_0$ (c) $4V_0q_0$ (d) $3V_0q_0$ (e) You cannot determine the work from this diagram alone.

4)

If $5.0\times 10^{21}$ electrons pass through a $20~\rm\Omega$ resistor in 10 min, what is the potential difference across the resistor?

(a) 21 V (b) 27 V (c) 32 V (d) 37 V (e) 54 V