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Barry Melby
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Homework Statement
A uniform magnetic field pointing in the positive z-direction fills a cylindrical volume of space of radius R whose central axis is the z axis. Outside this region, there is no magnetic field. The magnitude of the magnetic field in changes with time as B = Bmax sin(ωt).
a. Calculate the magnitude of the electric field that accompanies this changing magnetic field as a function of time t and radial distance rfrom the center of the magnetic field for r < R.
b. Calculate the magnitude of the electric field that accompanies this changing magnetic field as a function of time t and radial distance rfrom the center of the magnetic field for r>R.
Homework Equations
I'm not exactly sure which equations to use.
The Attempt at a Solution
a)
E(2*pi*r) = pi*r^2 (dB/dt)
E = r/2 (dB/dt)
E = [omega*r*Bmax(sin(omega*t))]/2
This however is incorrect. b)
E(2*pi*r) = pi*R^2 (dB/dt)
E = R^2/2r (dB/dt)
E = [omega*R^2*Bmax (cos(omega*t))]/2r
Which also appears to be incorrect. Where did I go wrong?