Question

A spatially uniform magnetic field B exists within a cylindrical volume of radius R, pointing into the page. at the rate of 10.0m. (i) Find the initial acceleration of a proton released at a point a directly below the center of the cylinder, at a radial distance of 5.00cm. The magnitude of this field is decreasing (ii) Now find the acceleration of an electron released at the same point. both parts. (HINT: Use your knowledge of Faraday's Law to first find Need both, magnitude and direction of this acceleration for Figure 1: the electric field at that point, then use that to find the force on a (10 - points) charged particle under consideration.)

Answer 1

4)

a) induced emf = A*dB/dt

E*2*pi*a = pi*a^2*dB/dt

E = (a/2)*dB/dt

= (0.05/2)*10*10^-3

= 2.5*10^-4 N/C (towards +x axis)

use, F = q*E

mp*a = q*E

a = q*E/mp

= 1.6*10^-19*2.5*10^-4/(1.67*10^-27)

= 2.40*10^4 m/s^2

direction : towards +x axis

ii) for electron,

use, F = q*E

me*a = q*E

a = q*E/me

= 1.6*10^-19*2.5*10^-4/(9.1*10^-31)

= 4.40*10^7 m/s^2

direction : towards -x axis