D.4 Induction (HL)：練習問題

A bar magnet is dropped vertically through a fixed horizontal copper ring. As the North pole of the magnet approaches the ring from above, what is the direction of the induced current in the ring when viewed from above, and what is the reason according to Lenz's law?

A graph shows the variation with time \(t\) of the magnetic flux \(\Phi\) through a coil rotating at a constant angular speed in a uniform magnetic field. Which of the following conditions describes the orientation of the coil when the magnitude of the induced electromotive force (emf) is at its maximum?

A uniform magnetic field \( B \) exists in a cylindrical region of radius \( R \). The field is increasing at a constant rate \( \frac{\Delta B}{\Delta t} = α \). A thin conducting wire loop of radius \( r \) is placed coaxially with the cylindrical region. What is the induced electric field strength \( E_{ind} \) at a point on the wire loop if \( r > R \)?

According to Faraday's law of induction, the magnitude of the electromotive force (emf) induced in a conducting loop is proportional to which of the following?

A long straight wire carries a steady current \(I\) upwards. A conducting square loop is moved at a constant velocity to the right, directly away from the wire. What is the direction of the induced current in the loop as seen from the front?

A square loop of side length \(0.050 \text{ m}\) is placed in a uniform magnetic field of \(0.30 \text{ T}\). If the plane of the loop is perpendicular to the field lines, calculate the magnetic flux through the loop.

A straight metal rod of length \(0.60 \text{ m}\) moves at a constant speed of \(3.0 \text{ m s}^{-1}\) perpendicular to a uniform magnetic field of \(0.20 \text{ T}\). Determine the induced emf in the rod and state the effect on the emf if the rod is instead moved parallel to the magnetic field.

A transformer with an efficiency of 85% has a primary voltage of \(240 \text{ V}\) and a secondary voltage of \(12 \text{ V}\). If the current in the secondary coil is \(5.0 \text{ A}\), calculate the power input to the primary coil and the current in the primary coil.

A bar magnet is dropped vertically through a stationary coil of wire that is connected to a sensitive voltmeter. The north pole of the magnet enters the coil first.

(a) State the direction of the induced current (clockwise or anticlockwise) as viewed from above as the north pole approaches the top of the coil.
(b) Explain your answer to part (a) with reference to Lenz's law.
(c) The magnet is dropped from a greater height above the coil. State and explain the effect, if any, on the magnitude of the peak induced emf.

A rectangular coil with 200 turns and dimensions \(0.10 \text{ m} \times 0.20 \text{ m}\) is placed in a uniform magnetic field of \(0.40 \text{ T}\). The plane of the coil is initially perpendicular to the field lines.

(a) Calculate the magnetic flux linkage through the coil in this initial position.
(b) The coil is rotated by \(90^{\circ}\) about an axis in its plane in a time of \(0.050 \text{ s}\). Calculate the average induced emf in the coil.
(c) State and explain how the magnitude of the induced emf would change if the rotation speed were doubled.