Force on a Moving Charge (CIE A Level Physics)

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. 6.1.

Fig. 6.1

Electrons enter the slice at right angles to face SRXY.

A potential difference, the Hall voltage V_H, is produced between two faces of the slice.

.......................................... and .......................................... [1]

[2]

The Hall voltage  is given by the expression

[1]

[2]

A proton of mass m and electric charge q enters a region of magnetic field at point P and exits at point Q, as shown in Fig. 1.1.

The speed of the proton at P is v. The path followed by the proton is a quarter of a circle.

Fig. 1.1

State whether the speed v is the same, more than, or less than, the speed of the proton at Q. Explain your answer.

Explain why the path of the proton is circular.  

Show that the radius of the circular path is given by 

where B is the magnetic flux density.

The speed of the proton at P is v = 3.2 × 10⁶ m s^–1 and the magnetic flux density is 0.21 T.

Show that the radius of the path is 16 cm.

Positive charges are seen passing through different magnetic fields. 

Determine the direction of the missing quantity between B, v and F for each:

Fig. 1.1 shows two parallel plates. The magnitude of the electric field between the plates is 2.6 × 10³ N C^–1 and is directed from the top plate to the bottom plate.

The shaded region represents a region of magnetic field that is perpendicular to the page.

Fig. 1.1

An electron enters the region between the plates with a speed of 3.0 × 10⁵ m s^–1 and experiences zero net force as it travels through to the other side.

Suggest whether a proton moving with the same speed through the plates experiences zero net force. Explain your answer.

Another electron enters the region between the plates at half the speed of the electron in (b). 

Suggest whether the motion of the electron would be different to the motion of the electron in (b). Explain your answer.