Description: Exercise 29.75 A conducting rod of length 54.3cm slides over two pa
ID: 2297741 • Letter: D
Question
Description: Exercise 29.75
A conducting rod of length 54.3cm slides over two parallel metal bars placed in a magnetic field with a magnitude of 1.23kG, as shown in the figure. The ends of the rods are connected by two resistors, R1=151? and R2=297?. The conducting rod moves with a constant speed of 7.89m/s.
7.89 m/s
a) What are the currents flowing through the two resistors?
Please include a multiplication sign (*) to indicate that two units are being multiplied.
i1= [Num] [Units]
i2= [Num] [Units]
b) What power is delivered to the resistors?
Please include a multiplication sign (*) to indicate that two units are being multiplied.
P= [Num] [Units]
c) What force is needed to keep the rod moving with constant velocity?
Please include a multiplication sign (*) to indicate that two units are being multiplied.
Fmag= [Num] [Units]
A conducting rod of length 54.3cm slides over two parallel metal bars placed in a magnetic field with a magnitude of 1.23kG, as shown in the figure. The ends of the rods are connected by two resistors, R1=151? and R2=297?. The conducting rod moves with a constant speed of 7.89m/s.
7.89 m/s
a) What are the currents flowing through the two resistors?
Please include a multiplication sign (*) to indicate that two units are being multiplied.
i1= [Num] [Units]
i2= [Num] [Units]
b) What power is delivered to the resistors?
Please include a multiplication sign (*) to indicate that two units are being multiplied.
P= [Num] [Units]
c) What force is needed to keep the rod moving with constant velocity?
Please include a multiplication sign (*) to indicate that two units are being multiplied.
Fmag= [Num] [Units]
Explanation / Answer
a) B = 1.23 kG = 0.123 T
emf induced in rod = E = B*l*v = 0.123 * 0.543 * 7.89 = 0.527 V
current through R1 =
i1 = E /R1 = 0.527 / 151 = 3.49*10^-3 A
current through R2 =
i2 = E/R2 = 0.527 / 297 = 1.774*10^-3 A
b) power delivered to resistors = E*i1 + E*i2
= E*(i1+i2) = 0.527*(3.49 + 1.774)*10^-3 = 2.774*10^-3 W
c) net current through the rod = i1 + i2 = 5.264*10^-3 A
so force required to move the rod with constant velocity
Fmag = (i1+i2)*l*B = 5.264*10^-3*0.543*0.123 = 3.516*10^-4 N