O2 997, Exam # 2 A coil of wire composed of 15 turns of wire, of radius 2 cm, is

Question

O2 997, Exam # 2 A coil of wire composed of 15 turns of wire, of radius 2 cm, is connected to battery by wire not shown in the diagram, and current flows in the the East. coil. Consider the center of the coil to be the origin; North is in the 12 direction. A compass placed at location (0.06, 0, 0) a deflects 45 to 2. Clearly ( a) What compass deflection (magnitude and di- rection) would you expect to see if he compass location were moved to (0. show your work and explain your reasoning. If you make any approximations, state them.

Explanation / Answer

given a coil of n = 15 turns of wire

radius r = 2 cm

center of coil is the origin

North is +z direction

compass location ( 0.06, 0, 0) deflects 45 deg to east

now, magnetic field of earth = Be = 5*10^-5 T

so as the compass moves to 45 deg

hence

magnetic field at the location of the compass due to the coil is B = 5*10^-5 T along -x axis

now magnetic field at the axis of a coil = 2*pi*k*n*i*r^2/(x^2 + r^2)^3/2 , where i is current in the coil

so, 5*10^-5 = 2*pi*10^-7*(15*i*0.02^2)/(0.06^2 + 0.02^2)^3/2

i = 3.3552 A

a. if compass is moved to location x = 0.18 m

then magnetic field due to the coil B' = 2*pi*10^-7*(15*3.3552*0.02^2)/(0.18^2 + 0.02)^3/2

B' = 2.1293*10^-6 T

Be = 5*10^-5 T

angle mate wrt north = theta

tan(theta) = B'/Be = 2.1293/10*5

theta = 2.438 deg

hence the compass will now deflect by 2.438 deg towards east in the current location

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