Question

A conducting bar of mass m=0.5 kg is moving with a leftward speed v

0
​
=4 m/s on two frictionless wires that are L=2 m apart and connected by a resistor R. The bar starts at a distance x
0
​
=8 m away from the resistor. A magnetic field B=5 T points out of the screen. What maximum value must R be so that the bar stops before hitting the resistor? No sig fig requirement as there is an exact answer; standard units (Ohms), 100 B out of screen

Answer 1

To find the maximum value of R, use Faraday's law of electromagnetic induction. Set the induced EMF equal to the EMF across the resistor and solve for R. The maximum value of R can be found when the induced current is at its maximum value.

Step-by-step explanation:

To find the maximum value of R, we need to determine the maximum current induced in the bar as it moves through the magnetic field. The induced current can be calculated using Faraday's law of electromagnetic induction. The induced EMF is given by the equation:

EMF = B * L * v

Where B is the magnetic field strength, L is the length of the bar, and v is the velocity of the bar. Since the bar stops before hitting the resistor, the induced EMF must be equal to the EMF across the resistor. This can be written as:

EMF = i * R

Where i is the induced current and R is the resistance of the resistor. Setting these two equations equal to each other and solving for R gives us:

R = (B * L * v) / i

Since we want the maximum value of R, we need to consider the case where the induced current is at its maximum value. This occurs when the bar is moving perpendicular to the magnetic field, which results in the maximum flux change and induced current. Therefore, the maximum value of R is given by:

R = (B * L * v) / Imax

where Imax is the maximum value of the induced current.