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 ? 3.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.20 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 = 4.40 cm from the center of the circular field region.

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(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 = 4.40 cm from the center of the circular field region.

(c) At what instant is this force equal to zero?

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Explanation / Answer

Force = E*q   (*where E=electric field, q=charge (of electron) = 1.602*10^-19 C )

To find force, first find E.

Emf = integral( E*ds) = - dB/dt

dB/dt = B*A (*where A=area)

A = (pi*R^2)

So, we can now solve for E, by taking the derivative of Emf:

integral( E*ds) = B*A becomes...

E = dB*A/ds

**note ds = 2pi*r1

We find dB by taking the derivative of B:

B = 9.00t3 3.00t2 + 0.800,

dB = 27t2 - 6t, at time t=2, so

dB = 96

Plugging dB and A into the equation for E we get:

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