A bar magnet and a wire loop carrying current \(I\) are arranged as shown above. In which direction, if any, is the force on the current loop due to the magnet?
Correct Answer: \( \boxed{\mathrm{A}} \)
Apply the right-hand rule for a current loop (solenoid rule). Curl the fingers of the right hand in the direction of the current around the loop. The thumb points toward the loop’s north pole.
From the current direction shown, the face of the loop nearest the bar magnet behaves as a south pole.
The end of the bar magnet facing the loop is labeled \(N\). Since opposite magnetic poles attract, the loop is pulled toward the magnet.
Equivalently, the magnetic dipole experiences a force in the nonuniform magnetic field of the bar magnet, causing it to move toward the stronger magnetic field near the magnet.
Therefore, the force on the current loop is toward the magnet, so the correct answer is (A).
Which of the following is NOT equal to one tesla?
Correct Answer: \( \boxed{\mathrm{E}} \)
From the magnetic force equation,
\( F=qvB \)
the SI unit of magnetic field is
\( 1\,\mathrm{T}=\dfrac{\mathrm{N}}{\mathrm{C}\cdot\mathrm{m/s}}=\dfrac{\mathrm{N}\cdot\mathrm{s}}{\mathrm{C}\cdot\mathrm{m}}=\dfrac{\mathrm{N}}{\mathrm{A}\cdot\mathrm{m}} \).
Therefore,
\( 1\,\mathrm{T}=\dfrac{\mathrm{N}}{\mathrm{A}\cdot\mathrm{m}}=\dfrac{\mathrm{J}}{\mathrm{A}\cdot\mathrm{m}^{2}}=\dfrac{\mathrm{kg}}{\mathrm{C}\cdot\mathrm{s}}=\dfrac{\mathrm{V}\cdot\mathrm{s}}{\mathrm{m}^{2}} \).
However,
\( \dfrac{\mathrm{A}\cdot\mathrm{N}}{\mathrm{V}}=\dfrac{\mathrm{A}\cdot\mathrm{N}}{\mathrm{J/C}}=\dfrac{\mathrm{A}\cdot\mathrm{N}\cdot\mathrm{C}}{\mathrm{J}}=\dfrac{\mathrm{A}\cdot\mathrm{C}}{\mathrm{m}} \),
which is not dimensionally equivalent to the tesla.
Therefore, the correct answer is (E).
Which of the following equations implies that it is impossible to isolate a magnetic pole?
Correct Answer: \( \boxed{\mathrm{C}} \)
Gauss’s law for magnetism states that
\( \displaystyle \oint \vec{B}\cdot d\vec{A}=0 \)
This equation says that the net magnetic flux through every closed surface is always zero.
Unlike electric charges, magnetic poles cannot exist independently. Every magnetic field line forms a closed loop, entering and leaving any closed surface in equal amounts.
Therefore, there are no magnetic monopoles, and it is impossible to isolate a single north or south magnetic pole.
In contrast:
• Choice (A) is Gauss’s law for electric fields.
• Choice (B) is Faraday’s law of induction.
• Choice (D) is the Ampère-Maxwell law.
Therefore, the equation that implies magnetic monopoles do not exist is \( \displaystyle \oint \vec{B}\cdot d\vec{A}=0 \).
Hence, the correct answer is (C).
