Question

A proton is held motionless between two horizontal metal plates 10 cm apart. What voltage should be applied between the plates?

Answer 1

Answer on Question #59521, Physics / Mechanics | Relativity

A proton is held motionless between two horizontal metal plates 10 cm apart. What voltage should be applied between the plates?

Solution:

$m = 1.67 \cdot 10^{-27} \ \mathrm{kg}$, mass of proton

$q = 1.6 \cdot 10^{-19} \ \mathrm{C}$, charge of proton

$d = 0.1 \ \mathrm{m}$

The gravitational force on a proton would be balanced by the electric field.

Balance of forces:

$$mg = \frac{qU}{d}$$

Therefore,

$$U = \frac{mgd}{q} = \frac{1.67 \cdot 10^{-27} \cdot 9.8 \cdot 0.1}{1.6 \cdot 10^{-19}} \approx 1 \cdot 10^{-8} \ V$$

Output: $1 \cdot 10^{-8} \ V$

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