Consider the circuit shown in the figure below. Assume that the rod slides to th

Question

Consider the circuit shown in the figure below. Assume that the rod slides to the right with a constant velocity.

a) What direction does the induced current flow through the resistor (up or down)?

b) Derive an equation for the current that runs through the resistor in terms of the variables given in the figure.

c) Find the electrical power dissipated by the resistor.

d) Assume that the rails and rod are perfect conductors (zero resistance). What force must be exerted on the rod in order to move it to the right with a constant velocity?

e)  Now assume that the rod is moved to the left with a constant velocity, repeat a - d.

Explanation / Answer

Here ,

a) as the flux in the loop is increasing

the current induced will be produce a field oposite to the applied field

the direction of induced current in the resistance is upwards

b)

for the current in the wire ,

Induced current = induced emf/R

Induced current = B*l * v/R

c)

power dissipated in resistance is

power dissipated = I^2 * R

power dissipated = (B*l * v/R)^2 * R

power dissipated = B^2 * v^2 * l^2/R

d)

for the force applied on the rod ,

F = B*I*L

F = B* B*l * v/R * l

F = B^2 * l^2 *v/R

the force exerted on the conductor is B^2 * l^2 *v/R

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