1] A square loop of wire, with sides of length 'a' lies in the first quadrant of the xy-plane, with one corner at the origin. In this region there is a non-uniform time-dependent magnetic field [itex]\vec B (y,t) = ky^3t^2\hat z[/itex]. Find the induced emf in the loop.(adsbygoogle = window.adsbygoogle || []).push({});

I applied the flux rule here.

[tex]\varepsilon = -{d\Phi \over dt} = -{d(\vec B \cdot \vec A) \over dt} = {d(Ba^2) \over dt} = -a^2\left({d(ky^3t^2)\over dt}\right)[/tex]

Am I going right here?

2] A perfectly conducting spherical shell of radius 'a' rotates about the z-axis with angular velocity [itex]\omega[/itex] in a uniform magnetic field [itex]\vec B = B_0\hat z[/itex]. Calculate the emf developed between the "north pole" and the equator.

I evaluted the flux here:

[tex]\Phi = \vec B \cdot \vec A = B_0\left(4\pi a^2\right)[/tex]

But the answer given here is: [tex]{1\over 2}B_0\omega a^2[/tex]

How do I incorporate [itex]\omega[/itex] in my flux?

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# Homework Help: 2 emf problems

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