Question 1

Multiple choiceHard1 mark

A circular loop of radius rr is in a uniform magnetic field of magnitude BB The angle between the field and the loop’s normal is 60∘60^\circ The radius is changed to 2r2r the field magnitude to B/2B/2 and the angle to 30∘30^\circ What is the ratio of the final magnetic-flux magnitude to the initial magnetic-flux magnitude?

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Answer: C. The magnetic-flux magnitude is Φ=BAcos⁡θ\Phi=BA\cos\theta and the loop’s area is proportional to r2r^2 Thus

ΦfinalΦinitial=12×4×cos⁡30∘cos⁡60∘=23.\frac{\Phi_{\mathrm{final}}}{\Phi_{\mathrm{initial}}} =\frac{1}{2}\times 4\times\frac{\cos30^\circ}{\cos60^\circ} =2\sqrt{3}.

A: reverses the ratio of the cosine factors.
B: uses the radius ratio as the area ratio, rather than squaring it.
D: omits the factor of 1/21/2 from the reduced field magnitude.
Remember: the angle in the flux expression is measured from the loop’s normal.

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