Question

A loop of wire with radius r=0.015 m is in a magnetic field with magnitude B as shown in the figure. B changes from B1 = 0.35 T to B2 = 4.5T in Δt=5.5s at a constant rate. The resistance of the wire is R=5Ω.

Part (a) Express the magnetic flux going through a loop of radius r assuming a constant magnetic field B. 

Part (b) Express the magnetic flux change, 40, in terms of B1, B2, and r. 

Part (c) Calculate the numerical value of ΔΦ in Tm² 

Part (d) Express the magnitude of the average emf, ε, induced in the loop in terms of ΔΦ and Δt. 

Part (e) Calculate the numerical value of the emf in V 

Part (f) Express the current induced in the loop. I, in terms of ε and R. 

Part (g) Calculate the numerical value of I in A.

Part (h) What's the direction of the current if you are looking down at the loop so that the magnetic field is coming towards you? 

Answer 1

A)

Flux, phi = B1 A

Phi = 0.35 x pi x 0.015^2 = 2.47 x 10^-4 Wb

B)

d(phi) = π r^2 (B2 - B1)

C)

d(phi) = pi x 0.015^2 (4.5 - 0.35) = 2.93 x 10^-3 Wb

D)

Emf, E = ΔΦ/Δt

E)

Emf, E = (2.93 x 10^-3)/5.5 = 5.33 x 10^-4 V

F)

Current, I = ε/R

G)

Current, I = 5.33 x 10^-4/5 = 1.07 x 10^-4 A

H)

Clockwise

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