A rod moves on two horizontal frictionless conducting rails, as shown. The magnetic field in the region is directed perpendicularly to the plane of the rails and is uniform and constant. If a constant force of 0.60 N moves the bar at a constant velocity of 2.0 m/s, what is the current through the 12- load resistor?

Question

A rod moves on two horizontal frictionless conducting rails, as shown. The magnetic field in the region is directed perpendicularly to the plane of the rails and is uniform and constant. If a constant force of 0.60 N moves the bar at a constant velocity of 2.0 m/s, what is the current through the 12- load resistor?

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Answer 1

To find the current through the 12-Ω load resistor, we need to use Ohm's Law, which states that the current flowing through a conductor is equal to the ratio of the voltage across it to its resistance.

In this case, the force applied to the rod is causing it to move at a constant velocity, indicating that the opposing force from the magnetic field is equal to the applied force. Therefore, the work done by the applied force is equal to the work done by the magnetic force.

The work done by the applied force is given by the equation:

Work (W) = force (F) x distance (d)

Given that the applied force is 0.60 N and the velocity is 2.0 m/s, we can determine the distance traveled by the rod using the equation:

distance (d) = velocity (v) x time (t)

Since we know the velocity (v) is 2.0 m/s, we need to find the time (t) it takes for the rod to travel the distance. Using the formula:

t = d / v

We can then substitute this value of time back into the equation for work done by the applied force to find the distance traveled by the rod.

Now, we can determine the work done by the magnetic force. The work done by a magnetic force is given by the equation:

W = magnetic force (B) x distance (d)

Since the magnetic force is perpendicular to the direction of displacement, the work done by the magnetic force is zero. Therefore, the work done by the applied force must be equal to the work done against the resistance in the circuit.

The work done against the resistance is given by the equation:

Work (W) = current (I) x resistance (R)

Given that the resistance is 12 Ω, we can determine the current flowing through the 12-Ω load resistor by rearranging the equation for work done against the resistance:

I = W / R

Now, we can substitute the value of work done by the applied force into the equation for current to find the current through the 12-Ω load resistor.