Question

m I Voltage source

1) In a simple device for measuring the magnitude B of a magnetic field, a conducting rod (length d = 1.5 m , mass m = 110 g ) hangs from a friction-free pivot and is oriented so that its axis of rotation is aligned with the direction of the magnetic field to be measured. Thin flexible wires (which exert negligible force on the rod) carry a current I = 10 A , which causes the rod to deflect an angle θ with respect to the vertical, where it remains at rest (see the figure)

What is the largest magnetic field magnitude that can be measured using this device?

B_max = __________________T

2) A coaxial cable consists of a solid inner conductor of radius R1 surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3 (the figure). The conductors carry equal and opposite currents I0distributed uniformly across their cross sections.

a) Determine the magnetic field at a distance R from the axis for R2<R<R3.

b) Let I0=1.50A, R1=1.00 cm, R2=2.00 cm, and R3=2.50 cm. Graph B from R=0 to R=3.00 cm

Answer 1

Given that d = 1.5 m, m = 110 g, I = 10 A Largest Magnetic field B = m g sin 90 degree /I d = 0.110 times 9.8 times 1/10 times 1.5 B = 0.0719 B = 0.0719 T \r\n From given data R_2 < R < R_3 I = I_0 - I_0 [(pi R^2 - pi R_2^2)/(pi R_3^2 - pi R_2^2)] Appling Amperes� law B (2 pi r) = mu_0 I_0 (R_3^2 - R^2) /(R_3^2 - R_2^2) B = [mu_0 I_0 (R_3^2 - R^2)]/[2 pi r (R_3^2 - R_2^2)]