CAIE A-Level Physics A2 20 Magnetic Fields Questions

An electron having charge -q and mass m is accelerated from rest in a vacuum through a potential difference V.
The electron then enters a region of uniform magnetic field of magnetic flux density B, as shown in Fig. 7.1.

The direction of the uniform magnetic field is into the plane of the paper.
The velocity of the electron as it enters the magnetic field is normal to the magnetic field. The radius of the circular path of the electron in the magnetic field is r.

The potential difference V in (c) is increased. The magnetic flux density B remains unchanged. By reference to the momentum of the electron, explain the effect of this increase on the radius r of the path of the electron in the magnetic field.

A thin slice of conducting material has its faces PQRS and VWXY normal to a uniform magnetic field of flux density B, as shown in Fig. 9.1.

Electrons enter the slice at right-angles to face SRXY.
A potential difference, the Hall voltage $V_{\mathrm{H}}$, is developed between two faces of the slice.

The Hall voltage $V_{\mathrm{H}}$ is given by the expression

State the meaning of the symbol n.

An electron is travelling in a vacuum at a speed of $3.4 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}$. The electron enters a region of uniform magnetic field of flux density 3.2 mT , as illustrated in Fig. 8.1.

The initial direction of the electron is at an angle of $30^{\circ}$ to the direction of the magnetic field.

When the electron enters the magnetic field, the component of its velocity $v_{\mathrm{N}}$ normal to the direction of the magnetic field causes the electron to begin to follow a circular path.

Calculate:

Calculate:
(i) $v_{\mathrm{N}}$