A thin circular coil of radius r= 15 contains N = 3 turns ofNichrome wire. A sma

Question

A thin circular coil of radius r= 15 contains N = 3 turns ofNichrome wire. A small compass is placed at the center of the coil,as shown below. With the battery disconnected, the compass needlepoints to the right, in the plane of the coil. Assume that thehorizontal component of the Earth's magnetic field is about BEarth= 2*10^-5 tesla. When the battery is connected, a current of 0.25 ampere runsthrough the coil. predict the deflection of the compass needle. Ifyou have to make any approximation, state what they are. Is thedeflection outward or inward as seen from above? what is themagnitude of the deflection?

Explanation / Answer

the magnetic field due to a circular coil is B = (oNI/2r) ----------(1) o = 4 * 10-7N/A2,N = 3 turns,I = 0.25 ampere and r = 15 cm = 15 *10-2 m the horizontal component of the Earth's magnetic fieldis BH = B * cos or cos = (BH/B) or = cos-1(BH/B) BH = 2 * 10-5 T and the value of B isobtained from equation (1)

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