Electromagnetism

Given efficiency is 90%, and the power supply is 3 kW, so the output power of the secondary coil is: We can now use the formula for power: From the given current in the secondary coil, A, so: Now, using the power formula for the primary coil: Using the efficiency, we find the primary current:

The force on a current-carrying wire in a magnetic field is given by: where is the current, is the length vector of the wire, and is the magnetic field.
The magnetic field in the problem is: The length vector of the wire is from to , so the length of the wire . Using the cross-product for and solving for the force, we find the value of in terms of time , giving the correct answer as .

Thus, the correct answer is (b).

The magnetic force on a moving charge is given by:

where is the charge, is the velocity of the charge, and is the magnetic field. This force is dependent on the angle between the velocity vector ( ) and the magnetic field vector ( ), as indicated by the cross product in the equation. When the charge is moving parallel to and opposite the magnetic field, the angle between and is 0°, meaning the sine of this angle, , is zero.

Since the force is proportional to the cross product of the two vectors, the force is zero when the vectors are either parallel or antiparallel. In this case, the charge does not experience any magnetic force because the velocity vector and the magnetic field vector do not create a perpendicular component to generate a force.

Thus, the magnetic force acting on the charge is zero in this situation, confirming that the correct answer is (d).

In a cyclotron, the frequency of the particle's revolution is given by: where is the charge of the particle, is the magnetic field, and is the mass of the particle. Rearranging to solve for , we get: Substitute the given values: Hence, the correct answer is (b).

In circuits with inductors, the current through the battery just after the switch is closed depends on the inductor's opposition to the change in current (due to its inductance).

- In circuit 1, the inductor is in series with the resistor, and the current is opposed by both the resistor and inductor.
- In circuit 3, the inductor is in parallel with the resistor, and the current through the battery will be larger compared to circuit 1 because the current bypasses the inductor through the parallel path.
- In circuit 2, the current through the inductor is opposed by the inductor's inductance, but the resistor provides a direct path for current flow.

Thus, the ranking of current through the battery from least to greatest is 1, 3, 2.