A 120-V battery is connected across two parallel metal plates of area 28.5 cm2 a

Question

A 120-V battery is connected across two parallel metal plates of area 28.5 cm2 and separation 8.20mm . 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 magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates?

Explanation / Answer

Part A)

Start with conservation of energy such that qV = .5mv2

(2)(1.6 X 10-19)(1800) = (.5)(6.64 X 10-27)(v2)

v = 4.17 X 105 m/s

To go through undeflected, apply v = E/B, so...

B = E/v and E = V/d

B = V/vd = (130)/(4.17 X 105)(8.3 X 10-3)

B = 3.81 X 10-2 T which is 38.1 mT

Part B)

Applying the right hand rule, we can determine that the magnetic field must point out of the page toward you. (Or you can call it the positive z direction)

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