Within the green dashed circle shown in the figure below, the magnetic field cha

Question

Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B = 8.00t3 1.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.15 cm.

(a) When t = 2.00 s, calculate the magnitude of the force exerted on an electron located at point P1, which is at a distance r1 = 4.30 cm from the center of the circular field region.
What is the magnetic flux through a circle of radius r1? N

(b) When t = 2.00 s, calculate the direction of the force exerted on an electron located at point P1, which is at a distance r1 = 4.30 cm from the center of the circular field region.

2

Tangent to the electric field line passing through point P1 and clockwise. Tangent to the electric field line passing through point P1 and counterclockwise.     The magnitude is zero.
(c) At what instant is this force equal to zero? (Consider the time after t = 0 s.)
3 s

Explanation / Answer

By maxwell equation

the change in magnetic field induce a electric field given by

E=-(dB/dt)*(r/2)

dB/dt=24t^2-2t

at t= 2 sec

B=60.8 T

dB/dt=92 T/s

E=-92*(0.043)/2=-1.978 N/C(- indicate direction of elecric field is opposite to direction of change in magnetic field)

force=qE=3.1648*10^(-19) N

magnetic flux =B*Area=60.8*3.142(0.043)^2=0.3531 T.m^2

(b)direction is tangent to direction of electric field but in opposite direction.i.e.at an angle of 180degree to electric field

(c)force will be 0 when dB/dt=0

24t^2-2t=0

2t(12t-1)=0

t=0 or t=1/12=0.0833 sec

so it becomes 0 at t=0.0833 sec

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