Within the green dashed circle shown in the figure below, teslas, t is in second

Question

Within the green dashed circle shown in the figure below, teslas, t is in seconds, and R 2.05 cm ,the magnetic field changes with time according to the expression 8 -6.00-2.00+0.800, where B is in R x (a) When t-2.00 s, calculate the magnitude of the force exerted on an electron located at point Pt, which is at a distance ry 4.10 cm from the center of the circular field regiorn (b) when t = 2.00 s, calculate the direction of the force circular field region O Tangent to the electric field line passing through point Ps and clockwise exerted on an electron located at point P., which is at a distance r,-4.10 cm from the center of the Tangent to the electric field line passing through point P, and counterclockwise. The magnitude is zero. (c) At what instant is this force equal to zero? (Consider the time after t-0 s)

Explanation / Answer

effective area, A = pi*R^2

= pi*0.0205^2

= 0.00132 m^2

B = 6*t^3 - 2*t^2 + 0.8

dB/dt = 18*t^2 - 4*t

a)

use Faraday's law,

induced emf = A*dB/dt

E*2*pi*r1 = A*(18*t^2 - 4*t)

E = A*(18*t^2 - 4*t)/(2*pi*r1)

at t = 2s

E = 0.00132*(18*2^2 - 4*2)/(2*pi*0.041)

= 0.328 N/c

so, Force acting electron, F = q*E

= 1.6*10^-19*0.328

= 5.25*10^-20 N

b) tangent to the electric field line passing through point P1 and clockwise

c) when E = 0, F = 0

E = A*(18*t^2 - 4*t)/(2*pi*r1)

0 = A*(18*t^2 - 4*t)/(2*pi*r1)

18*t^2 = 4*t

18*t = 4

t = 4/18

= 0.222 s

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