The magnetic force on a charge \( Q \) moving with velocity \( \mathbf{v} \) is
Answer: A
The cross product makes the force perpendicular to both the velocity and the field, so it changes the direction of motion but never the speed. Adding the electric term \( Q\mathbf{E} \) gives the complete Lorentz force.
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A charged particle moving parallel to a magnetic field experiences
Answer: B
The cross product vanishes when the velocity and the field are parallel, so the particle continues in a straight line. The force is greatest when the motion is at right angles to the field, and varies as the sine of the angle between them.
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A charged particle entering a uniform magnetic field at right angles to it moves in
Answer: C
The force is always perpendicular to the velocity, so it supplies exactly the centripetal force of circular motion and does no work. A component of velocity along the field would turn the circle into a helix of constant pitch.
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The radius of the circular path of a particle of mass \( m \) and charge \( Q \) moving at speed \( v \) perpendicular to a field \( B \) is
Answer: D
Equating the magnetic force to the centripetal force gives this result at once. It is the basis of the mass spectrometer, since particles of the same charge and speed separate by mass, and of the cyclotron, whose period turns out to be independent of the speed.
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The magnetic force on a charged particle does
Answer: A
A force at right angles to the displacement contributes nothing to the work integral, so the speed and the kinetic energy are unchanged however long the particle spends in the field. Only the electric part of the Lorentz force can change a particle's energy.
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The force on a straight conductor of length \( L \) carrying current \( I \) in a uniform field \( B \) is
Answer: B
The vector form is \( I\mathbf{L} \times \mathbf{B} \), so the force is greatest when the conductor lies across the field and zero when it lies along it. The force is perpendicular to both, which is what makes a motor turn.
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Two long parallel conductors carrying currents in the same direction
Answer: C
Each lies in the circumferential field of the other, and working out the cross product shows the force to be inward. This is the reverse of the electrostatic case, where like charges repel, and it was formerly the basis of the definition of the ampere.
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The force per unit length between two long parallel conductors is proportional to
Answer: D
The field of one falls as the inverse first power of distance and the force on the other is proportional to that field, so the force per unit length does too. A short-circuit current of tens of kiloamperes therefore produces forces on busbars that the mechanical design must withstand.
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The torque on a current loop of magnetic moment \( \mathbf{m} \) in a uniform field is
Answer: A
The magnitude is the moment times the field times the sine of the angle between them, so the torque is greatest when the loop plane contains the field and zero when the moment is aligned with it. That aligned position is the one of stable equilibrium.
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A current loop in a uniform magnetic field experiences
Answer: B
The forces on opposite sides of the loop are equal and opposite, so they cancel as a resultant but constitute a couple. A net force appears only in a non-uniform field, which is why a small magnet is drawn toward the pole of a larger one.
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