An elastic circular conducting loop expands at a constant rate over time such th

Question

An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t) = r0 + vt, where r0 = 0.175 m and v = 0.0100 m/s. The loop has a constant resistance of R = 12 ? and is placed in a uniform magnetic field of magnitudeB0 = 0.900 T, perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, i, at t = 5 s.

Explanation / Answer

Area A = pi*r^2 = pi * ( r0 + vt) ^2 B = 0.9 T so flux = B*A = 0.9* pi * ( r0 + vt)^2

magnitude of Induced emf = |d(B*A)/dt| = 0.9*pi*2* ( r0+vt)*v = 0.9*pi*2* ( 0.175 + 0.01*5)*0.01 = 0.01272 V

so induced current = 0.01272 / 12 = 0.00106 A

direction of induced current is clockwise as seen from above

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.