Question

(11%) Problem 5: A time-dependent but otherwise uniform magnetic field of magnitude Bo(t) is confined in a cylindrical region of radius 7.5 cm. Initially the magnetic field in the region is pointed out of the page and has a magnitude of 2.5 T, but it is decreasing at a rate of 3.5 G/s. Due to the changing magnetic field, an electric field will be induced in this space which causes the acceleration of charges in the region. O B.(t) o o O P O ------ o ~ 50% Part (a) What is the direction of the acceleration of a proton placed at the point P1,3.5 cm from the center? Counterclockwise ✓ Correct! A 50% Part (b) What is the magnitude of this acceleration, in meters per square second? a Grade Summary Deductions 0% Potential 100%

Answer 1

Part (b) R R = 7.5cm r = 3.5cm According to faraday's law do dt do Eds ar d E(2 x ) = - * (BAcosoº) dt E(2 x Tr) = dB dt E(2 x ) = 2 dB - 77 dt E = dB dt 2 1G = 10-41 Magnitude of electric field at P

3.5 x 10-2 E = * (-3.5 x 10-4) 2 E = 6.125 x 10-6 N/C Acceleration of proton at P eE a = m 1.6 10-19x6.125 x 10-6 a = 27 1.67 x 10 a = 586.8 x m/s2