Answer to Question #91102 in Electricity and Magnetism for Promise Omiponle

Question

100V battery is connected across 2 parallel plates of distance 8mm. A proton starts from rest and pass through plates which has 1.5kV potential difference. If the proton passes the plates without deflection, find the magnitude of B.

Answer 1

Proton velosity is

$$v = (\frac{2eU}{m})^{0.5} = (\frac{2\cdot1.6\cdot15}{1.67})^{0.5}10^{5} = 0.54(Mm/s).$$

There will be no deflection if

$$Bv = E,$$

i.e.

$$B = \frac{U_1}{dv} = \frac{0.1}{8\cdot0.54} = 23 (mT)$$