A V = 130-V battery is connected across two parallel metal plates of area 28.5 c

Question

A V = 130-V battery is connected across two parallel metal plates of area 28.5 cm2 and separation 8.30 mm . A beam of alpha particles (charge +2e, mass 6.64×1027 kg) is accelerated from rest through a potential difference of 1.70 kV and enters the region between the plates perpendicular to the electric field, as shown in the figure.(Figure 1)

Part A

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

https://session.masteringphysics.com/problemAsset/1266170/12/pic1.jpg

Explanation / Answer

Accelerating Voltage = V1=1.70 kV = 1700 V

Charge on alpha= q=3.2*10^-19 C

Mass = m =6.64*10^-27 kg

Kinetic energy = electric potential energy

(1/2)mv^2 = qV

v = sq rt [2qV/m]

The alpha particles will emerge undeflected from between the plates if magnetic force=elctric force

qvB =qE

E = Vo/d

B = E /v

B =(Vo/d) sq rt [m/2qV]

B=130/(8.30/1000)*sqrt2*3.2*10^-19*1700/(6.64*10^-27)

B =0.03869 T

B =3.869*10^-2 T

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