D.2 電場與磁場：練習題

Which of the following best describes the direction of the magnetic force acting on a positive point charge moving with a velocity \(v\) perpendicular to a uniform magnetic field \(B\)?

A straight wire of length \(L\) carries a steady current \(I\) and is placed in a uniform magnetic field of strength \(B\). The wire makes an angle of \(30^{\circ}\) with the direction of the magnetic field. Which expression correctly gives the magnitude of the magnetic force acting on the wire?

A proton enters a region where a uniform electric field \(E\) and a uniform magnetic field \(B\) are perpendicular to each other. The proton's velocity is perpendicular to both fields. If the proton passes through the region without being deflected, what is its speed \(v\)?

What is the magnitude of the electric force acting on a point charge of \(+2.5 \mu\text{C}\) placed in a uniform electric field of strength \(4.0 \times 10^3 \text{ N C}^{-1}\)?

Two large, parallel horizontal metal plates are separated by a distance \(d\) in a vacuum. A potential difference \(V\) is maintained between the plates. A small particle with a positive charge \(q\) is held stationary exactly midway between the plates. What is the magnitude of the electric force acting on the particle when it is released?

Define the term electric field strength at a point in space and state its SI unit.

A straight wire of length \(0.50 \text{ m}\) carries a current of \(2.0 \text{ A}\) at an angle of \(30^\circ\) to a uniform magnetic field of strength \(0.40 \text{ T}\). Calculate the magnitude of the magnetic force acting on the wire.

Explain the mathematical and physical relationship between the electric field strength \(E\) and the electric potential gradient \(\frac{dV}{dr}\) at a point in space.

A straight horizontal wire of length \( 0.20 \text{ m} \) carries a current of \( 3.5 \text{ A} \). The wire is placed in a uniform magnetic field of strength \( 0.15 \text{ T} \) that is directed vertically upwards.

(a) Calculate the magnitude of the magnetic force acting on the wire if it is oriented perpendicular to the magnetic field.
(b) State the magnitude of the force if the wire is rotated so that it is parallel to the magnetic field lines.
(c) Use Fleming's Left-Hand Rule to describe the orientation of the force relative to the current and the magnetic field when they are perpendicular.

Two point charges, \(Q_1 = +5.0 \text{ nC}\) and \(Q_2 = +5.0 \text{ nC}\), are positioned at coordinates \((-3.0 \text{ cm}, 0)\) and \((+3.0 \text{ cm}, 0)\) respectively in a Cartesian plane.

(a) Calculate the electric potential at a point \(P\) located at \((0, 4.0 \text{ cm})\).
(b) Determine the magnitude and direction of the net electric field at point \(P\).
(c) A third charge \(q = -1.0 \text{ nC}\) is moved from infinity to point \(P\). Calculate the work done by the external agent in this process.