A circular loop of area A is placed perpendicular to a time-varying magnetic fie

Question

A circular loop of area A is placed perpendicular to a time-varying magnetic field of B(t) = B0 + at + bt2, where B0, a, and b are (positive) constants. (a) What is the magnetic flux through the loop at t = 0? (Use the following as necessary: B0, a, b, and A.) ?B = (b) Derive an equation for the induced potential difference in the loop as a function of time. (Use the following as necessary: B0, a, b, A, and t.) Vind = (c) What is the magnitude and the direction of the induced current if the resistance of the loop is R? (Let the magnetic field point into the page, and the circular loop be in the plane of the page. Use the following as necessary: B0, a, b, A, t, and R.) magnitude iind = direction

Explanation / Answer

a) flux = B A = B0 A b) emf = dflux/dt= A dB/dt = A (B0 + a + 2bt) c) I = emf /R =A (B0 + a + 2bt)/R counter clockwise

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