A V = 160-V battery is connected across two parallel metal plates of area 28.5 c

Question

A V = 160-V battery is connected across two parallel metal plates of area 28.5 cm2 and separation 8.50 mm. A beam of alpha particles (charge +2e, mass 6.64×1027 kg) is accelerated from rest through a potential difference of 1.80 kV and enters the region between the plates perpendicular to the electric field.

Part A

What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates?

A V = 160-V battery is connected across two parallel metal plates of area 28.5 cm2 and separation 8.50 mm. A beam of alpha particles (charge +2e, mass 6.64×1027 kg) is accelerated from rest through a potential difference of 1.80 kV and enters the region between the plates perpendicular to the electric field.

Part A

What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates?

Explanation / Answer

for beam,

delta(KE) = q deltaV

(6.64 x 10^-27) v^2 / 2 = (2 x 1.6 x 10^-19) (1.80 x 10^3)

v = 4.165 x 10^5 m/s

now , field inside the capacitor E = V /d = (160)/(8.50 x 10^-3)

E = 18823.5 V/m

for particle to move undeflected,

E = v B

B = (18823.5) / (4.165 x 10^5)

B = 0.045 T

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