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 10.00t3 3.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.35 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 ri4.70 cm from the center of the circular field region 3.187E-19x 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 4.70 cm from the center of the circular field region O Tangent to the electric field line passing through point Pi and clockwise. O Tangent to the electric field line passing through point P1 and counterclockwise. O The magnitude is zero (c) At what instant is this force equal to zero? (Consider the time after t=0s.) 0.2

Explanation / Answer

a )

B = 10 t3 - 3 t2 + 0.8

R = 2.35 cm = 0.0235 m

t = 2 sec

r1 = 4.7 cm = 0.047 m

dB/dt = 30 t2 - 6t

e = 3.14 X R2 X (30 t2 - 6t)

E X 2 X 3.14 X r1 = 3.14 X R2 X (30 t2 - 6t)

E = 3.14 X R2 X (30 t2 - 6t) / 2 X 3.14 X r1

E = R2 X (30 t2 - 6t) / 2 X r1

E = 0.02352 X ( 30 X 22 - 6 X 2 ) / 2 X 0.047

E = 0.6345 N/C

b )

it is a clockwise direction because of usin gright hand rule

thumb will be into the page.

c )

(30 t2 - 6t) = 0

30 t2 = 6t

30 t= 6

t = 6/30 = 0.2 sec

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