Question

The figure shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.40 m. The rails are connected by a 10.5-Ω resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.750 T.

Find the speed at which the bar must be moved to produce a current of 0.125 A in the resistor

Answer 1

The speed at which the bar must be moved to produce a current of 0.125 A in the resistor is 4.375 m/s.

Step-by-step explanation:

To find the speed at which the bar must be moved to produce a current of 0.125 A in the resistor, we can use Ohm's law and Faraday's law of electromagnetic induction. Ohm's law states that the current flowing through a resistor is equal to the voltage across the resistor divided by its resistance. In this case, the resistor has a resistance of 10.5 Ω. Therefore, the voltage across the resistor can be found by multiplying the current (0.125 A) by the resistance (10.5 Ω), which gives us 1.3125 V.

Faraday's law of electromagnetic induction states that the induced voltage in a conductor is equal to the rate of change of magnetic flux through the conductor. The magnetic flux can be calculated by multiplying the magnetic field strength (0.750 T), the length of the rod (0.40 m), and the speed of the rod. Since we want to find the speed, we can rearrange the formula to solve for it:

v = V / (B * L)

Plugging in the values, we get:

v = 1.3125 V / (0.750 T * 0.40 m) = 4.375 m/s

Therefore, the speed at which the bar must be moved to produce a current of 0.125 A in the resistor is 4.375 m/s.

Answer 2

emf = V = IR = 10.5 *.125
emf = d (flux) /dt = B * dA/dt = B * .4 * dx/dt
10.5 ohm*.125 A = .750 T *.4m * (X m/s)