For the situation described in figure, the magnetic field is directed into the p

Question

For the situation described in figure, the magnetic field is directed into the page and varies as

a. Calculate the magnitude of the force exerted on an electron located at point P when t = 2.09 s. Answer in units of N.

b. What is the direction of the force?
   1. same as that of the electric field
   2. opposite to that of the magnetic field
   3. perpendicular to that of the electric field and magnetic field
   4. same as that of the magnetic field
   5. opposite to that of the electric field
   6. Insufficient information is given.

c. At what (non-zero) time is this force equal to zero? Answer in units of s.

Explanation / Answer

Given,

B = dt^3 - at^2 + b ; r = 4.4 cm ; R = 1.6 cm

B = 2 t^3 - 1.77 t^2 + 0.694

dB/dt = 6 t^2 - 3.54 t + 0

for t = 2.09 s

dB/dt = 6 x 2.09^2 - 3.54 x 2.09 = 18.81 T/s

we can relate the electric and changing magnetic field as:

E(2 pi r) = dB/dt x pi R^2

E = dB/dt x R^2/2 r = 18.81 x 0.016^2/2 x 0.044 = 0.055 N/C

F = e E = 1.6 x 10^-19 x 0.055 = 8.8 x 10^-21 N

Hence, F = 8.8 x 10^-21 N

b)1. same as that of the electric field

c)set dB/dt = 0

6 t^2 - 3.54 t = 0 => t = 3.54/6 = 0.59 s

Hence, t = 0.59 s

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