First slide

Electrostatic potential energy

Question

An electron beam accelerated from rest through a potential difference of 5000 V in vacuum is allowed to impinge on a surface normally. The incident current is 50 $μ$ A and if the electrons come to rest on striking the surface, the force on it is

Difficult

A

$1.1924 \times 10^{- 8} N$
B

$2.1 \times 10^{- 8} N$
C

$1.6 \times 10^{- 8} N$
D

$1.7 \times 10^{- 8} N$

Solution

$\begin{array}{l} Energy = \frac{1}{2} m v^{2} = 5000 eV \\ = 5000 \times 1.6 \times 10^{- 19} joule \\ m v = \sqrt{2 \times 5000 \times (1.6 \times 10^{- 19}) m} = 4 \times 10^{- 8} \sqrt{m} \end{array}$
$= n = \frac{q}{e} = \frac{I t}{e} = \frac{50 \times 10^{- 6} \times 1}{1.6 \times 10^{- 19}} = 31.25 \times 10^{13}$
Force = change of momentum per second
$= n m v = 31.25 \times 10^{13} \times 4 \times 10^{- 8} \sqrt{m} = 1.1924 \times 10^{- 8} N$

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