IB Physics HL Theme D: Fields questions

Exam-style multiple choice and written questions with full markschemes. Check multiple choice answers straight away, or type, photograph or draw a written answer and get it marked.

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Question 1

Multiple choiceHard1 mark

A straight horizontal conductor of length 0.50 m0.50\ \mathrm{m} carries a current of 2.0 A2.0\ \mathrm{A} northeast; its eastward:northward direction-component ratio is 3:43:4 A uniform horizontal magnetic field of magnitude 0.50 T0.50\ \mathrm{T} points northeast, with eastward:northward direction-component ratio 4:34:3 What are the magnitude and direction of the force on the conductor?

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Answer: C. The current and field directions are 53.1∘53.1^\circ and 36.9∘36.9^\circ north of east, so the angle between them is 16.2∘16.2^\circ with sin⁡θ=0.28\sin\theta=0.28 Thus F=BILsin⁡θ=(0.50)(2.0)(0.50)(0.28)=0.14 NF=BIL\sin\theta=(0.50)(2.0)(0.50)(0.28)=0.14\ \mathrm{N} Fleming’s left-hand rule gives a downward force.

A: gives the correct magnitude but reverses the force direction.
B: uses cos⁡θ\cos\theta giving 0.48 N0.48\ \mathrm{N} and reverses the force direction.
D: uses cos⁡θ\cos\theta giving 0.48 N0.48\ \mathrm{N} but gives the correct direction.
Remember: the force depends on the component of the current direction perpendicular to the magnetic field.

Question 2

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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