A 140-V battery is connected across two parallel metal plates of area 28.5cm^2 a

Question

A 140-V battery is connected across two parallel metal plates of area 28.5cm^2 and separation 8.50mm . A beam of alpha particles (charge+2e , mass 6.64*10^-27kg ) is accelerated from rest through a potential difference of 1.80kV and enters the region between the plates perpendicular to the electric field. What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates? What direction of magnetic field is needed so that the alpha particles emerge undeflected from between the plates if the charges are moving to the right and the electric field points upward?

Explanation / Answer

V = 140-V, A = 28.5 cm^2, d = 8.50 mm, q = +2e, m = 6.64*10^-27 kg, V' = 1.80 kV, find the magnitude of magnetic field B.

speed = v

qV = mv2/2, so v = (2qV/m) = 1.16*105 m/s

E = V'/d = 2.12*105 V/m

qE = qvB, B = E/v = 1.83 T

The direction of magnetic field is out of page if the charges are moving to the right and the electric field points upward.

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