A charged particle moves in a circular path in a uniform magnetic field. Which physical quantity remains constant throughout the motion?
Speed
The magnetic force on a moving charge is \(\vec{F} = q(\vec{v} \times \vec{B})\), which is always perpendicular to the velocity.
A force perpendicular to velocity does no work: \(W = \vec{F} \cdot \vec{d} = 0\), so the kinetic energy \(\frac{1}{2}mv^2\) and hence the speed stay constant.
The force only bends the path, giving uniform circular motion of radius \(r = \frac{mv}{qB}\).
The direction of velocity, and therefore the direction of momentum, changes continuously around the circle.
The magnetic force has constant magnitude qvB, but its direction keeps pointing toward the centre, so the force vector is not constant.
Hence, the answer is Speed.
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Important Questions from Motion in a Magnetic Field
Which of the following is the correct expression for cyclotron frequency?
The radius of curvature of a charged particle's passage in a homogeneous magnetic field is proportional to:
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A proton and an alpha particle moving with same kinetic energy enter in the region of uniform magnetic field perpendicular to it. The ratio of radii of their trajectories will be:
- A 2.0 m long metallic rod is rotated with an angular frequency of 100 rad/s about an axis normal to the rod and passing through its one end. A uniform magnetic field of 2.0 T exits parallel to the axis. The emf induced between the two ends of the rod is:
