In a simple device for measuring the magnitude B of a magnetic field, a conducti
ID: 1601332 • Letter: I
Question
In a simple device for measuring the magnitude B of a magnetic field, a conducting rod (length d = 0.80 m, mass m = 140 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 = 12 A, which causes the rod to deflect an angle theta with respect to the vertical, where it remains at rest (see the figure). (Figure 1) If theta = 17 degree, determine B. Express your answer to two significant figures and include the appropriate units. What is the largest magnetic field magnitude that can be measured using this device? Express your answer to two significant figures and include the appropriate units.Explanation / Answer
B) amgnetic force acting on the rod, FB = B*I*d*sin(0)
= B*I*d
In the equilibrium, the net torque acting on the rod = 0
FB*(d/2)*sin(90) - m*g*(d/2)*sin(17) = 0
B*I*d*(d/2) - m*g*d*sin(17)/2 = 0
B*I*d - m*g*sin(17) = 0
B = m*g*sin(17)/(I*d)
= 0.14*9.8*sin(17)/(10*0.8)
= 0.0501 T
= 50.1 mT
C) FB_max = m*g
Bmax*I*d = m*g
B_max = m*g/(I*d)
= 0.14*9.8/(10*0.8)
= 0.1715 T
= 171.5 mT