Question

Calculate the number of electrons that appear on the surface of the cathode plate when the jockey is connected at the end P of the potentiometer wire. Assume that no radiation is falling on the plates

• A. $8.85\times {10}^6$
• B. $11.0625\times {10}^9$
• C. $8.85\times {10}^9$
• D. 0

Answer 1

The correct option is C $8.85\times {10}^9$

The internal resistance and the potentiometer are in parallel, therefore the resistance in the circuit:

$R=\frac{2\times 8}{2+8}=\frac{16}{10}=1.6\Omega$

Using Thevenin's theorem, the voltage across the vacuum tube=

$V=\frac{20\times 8}{2+8}=\frac{160}{10}=16V$

charge collected across the vacuum tube:

$Q=CV=\frac{{\epsilon }_{\circ }A}{d}\times V=\frac{8.85\times {10}^{-12}\times 50\times {10}^{-4}}{0.5\times {10}^{-3}}=1.416\times {10}^{-9}$

$Q=ne\therefore n=\frac{Q}{e}=8.85\times {10}^9$