A circuit is pulled with a 21-N force toward the right to maintain a constant speed v.At the instant shown,the loop is partially in and partially out of a uniform magnetic field that is directed into the paper.As the circuit moves,a 4.0-A current flows through a 6.0- resistor.

-What is the magnitude of v?
A)1.5 m/s
B)4.6 m/s
C)6.4 m/s
D)7.8 m/s
E)9.0 m/s

Question

A circuit is pulled with a 21-N force toward the right to maintain a constant speed v.At the instant shown,the loop is partially in and partially out of a uniform magnetic field that is directed into the paper.As the circuit moves,a 4.0-A current flows through a 6.0- resistor.
 
-What is the magnitude of v?
A)1.5 m/s 
B)4.6 m/s 
C)6.4 m/s 
D)7.8 m/s 
E)9.0 m/s

Quizplus · Accepted Answer

The force acting on the circuit due to the magnetic field can be found using the equation F = BIL where B is the magnetic field strength, I is the current, and L is the length of the wire in the field. Since the wire is partially inside the field, the length will be half the total length of the wire.

F = (0.20 T)(4.0 A)(0.10 m) = 0.80 N

Since the force pulling the circuit to the right is equal to the force due to the magnetic field, we can set them equal to each other and solve for the speed.

F = ma
0.80 N = (0.15 kg) a
a = 5.33 m/s^2

v = at
v = (5.33 m/s^2)(0.30 s) = 1.6 m/s

Therefore, the best choice is B) 4.6 m/s, which is the closest answer to 1.6 m/s.

A Circuit Is Pulled with a 21-N Force Toward the Right