A square loop of side a shown schematically in Figure 3 is made out of a thin cy
ID: 2123936 • Letter: A
Question
A square loop of side a shown schematically in Figure 3 is made out of a thin cylindrical conducting wire, whose own radius is r << a and material%u2019s resistivity p. The loop is in the plane perpendicular to the uniform external magnetic field %u03B2 of unknown magnitude B. The loop contains a small device (%u201CQ-meter%u201D) that can measure the charge that passes through it over time. After the magnetic field was turned off, it was noted that the total charge passes through the Q-meter was equal to q. Based on this measurement do you think you would be able to find the original magnitude of B of the magnetic field?
A square loop of side a shown schematically in Figure 3 is made out of a thin cylindrical conducting wire, whose own radius is rExplanation / Answer
emf = dflux/dt
emf = B A/dt = B pi a^2/dt
emf = I R = I rho Awire/L = I rho pi r^2/(2 pi a) = B pi a^2/dt
but I = q/dt
so
q/dt rho pi r^2/(2 pi a) = B pi a^2/dt
q rho r^2/2 = B pi a^3
q = 2 B pi a^3/( rho r^2)
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