A 160 V battery is connected across two parallel metal plates of area 28.5 cm^2

Question

A 160 V battery is connected across two parallel metal plates of area 28.5 cm^2 and separation 8.40 mm. A beam of alpha particles (charge + 2e, mass 6.64 imes 10^ - 27 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. What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates?

http://session.masteringphysics.com/problemAsset/1266170/10/zaq.jpg

Explanation / Answer

so in a capacitor, E=V/d=160/8.4E-3=19048 N/C now lets find the speed of the alpha particles we use conservation of energy qV=1/2 m v^2 2*1.6E-19*1.7E3=0.5*6.64E-27*v^2 so v=404791 m/s then we use that we need F electric= F magnetic q E = q v B so B=E/v= 19048/404791=0.047 T

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