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 = 9.00t3 ? 2.00t2 + 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.
1 . _________ 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

Explanation / Answer

Given

magnetic field

B = 9.00t3 ? 2.00t2 + 0.800

dB /dt    = 27 .0 t2    - 4.0 t

induced emf     ?   = d?B /dt      = A dB/dt     =   ?R2 dB/dt  

According   to Faradyas   Law

E ( 2?r1 )   =    ?R2 dB/dt   

Electric field   at point   P1 is   E    =   ?R2 dB/dt    / ( 2?r1 )

E    =   R2 dB/dt   / ( 2r1)   = 0.5375 N/C

Here   R   = 0.0215 m     , r1   = 0.043 m

at   time t    = 2.0 sec

Force on the electron   F   = eE

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

then F   = 8.6*10^-20 N

(b) According to   right hand rule   the direction of force is clock wise direction

(c) the magnetic force on the electron is zero when

dB /dt    = 27 .0 t2    - 4.0 t     =0

solving for t we get   t = 0.148 sec

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