I will rate lifesaver for a correct answer!! A magnetic field directed into the

Question

I will rate lifesaver for a correct answer!!


A magnetic field directed into the page changes with time according to
B = 0.027 0t2 + 1.40,
where B is in teslas and t is in seconds. The field has a circular cross section of radius
R = 2.50 cm

(a) When
t = 4.20 s
and
r2 = 0.020 0 m,
what is the magnitude of the electric field at point
P2?

I am sorry there is no picture. all it is is a circle with a B field into the page. P2 is inside the circle, distance r2 from the center. There is a P1 outside of the circle distance r1 from the circle also but I do not think that has anything to do with this part. The radius of the circle is designated by R.

Please show work and final answer! Thank you!

Explanation / Answer

The radius, r = 0.02 m Time, t = 4.20 s The given magnetic field, B = ( 0.027t2 + 1.4 ) T By differenting the above with respect to time on both sides we get    dB/dt = 0.054t   ------------- (1) We have an equation for emf as        e = A(dB/dt) = r2(dB/dt) ------------(2) We also have an equation for emf = E*d = E * 2r --------(3) From (2) and (3) we have          E * 2r = r2(dB/dt)          E = r(dB/dt) / 2 = 0.02*0.054*4.2/2 = 0.0023 N/C

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