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 teslas, t is in seconds, and R 2.60 cm. 6.00t3-3.00t0.800, where B is in Bin (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 = 5.20 cm from the center of the circular field region (b) When t2.00 s, calculate the direction of the force exerted on an electron located at point P1, which is at a distance r15.20 cm from the center of the circular field region Tangent to the electric field line passing through point Pi 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.)

Explanation / Answer

a)

Given magnetic field

B = 6t3 3t2 + 0.8

dB /dt    =18t2-6t

induced emf is given by

E= A dB/dt = piR2 dB/dt   

According to Faradyas   Law

E ( 2pir1 ) = piR2 dB/dt    

Electric field   at point   P1 at t=2

E=(R2/2r1) dB/dt=(2.62/2*5.2)*(18*22-6*2)

E =39 N/C

Force on the electron  

F   = eE  

charge of the electron e= 1.6*10^-19 C

F=39*1.6*10-19=6.24*10-18 N

(b)

Tangent to the electric field line passing through point P1 and clockwise.

(c)

the magnetic force on the electron is zero when

dB /dt =18t2-6t=0

t=(6/18)=0.3333 s

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