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 8-4.003 - 1.002 +0.800, where 8 is in teslas, t is in seconds, and R-2.40 cm Xx ox (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 4.80 cm from the center of the circular field region. (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 r 4.80 cm from the center of the circular field region Tangent to the electrie 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-0 s.)

Explanation / Answer

B=4.00t31.00t2+0.800

dB/dt=12.00t22.00t

(a) We can use Faraday's law in integral form to find the induced electric field caused by the changing magnetic field:

On the left side of the equation, we know that the E-field must circulate around the changing magnetic field. On the right side, we need to look at the change in the magnetic flux, which will be the rate of change of the magnetic field times the area it exists in (as long as the loop we are integrating over is outside of the field).

E=(dB/dtR2) / (2r1)

Using the value for E we find above, we know that the force on an electron is:

F=qE=42.24e19N

(b) The force is tangent to the electric field line passing through point P1 and clockwise.

(c) This force equals zero when dB/dt =0:

0=12t22t

t=1/6sec

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