Quick questions on Magnetic fields and the Lorentz force on charges: VCE Physics Unit 3

A magnetic field $B$ is a vector at each point in space, measured in tesla (T). Field lines run from the north pole of a magnet to its south pole externally (and from south to north inside the magnet, forming closed loops). They never start or end on a charge; magnetic monopoles do not exist.

A charged particle moving with velocity $v$ through a magnetic field $B$ experiences a force:

When a charged particle moves perpendicular to a uniform $B$, the constant magnitude of $F = qvB$ supplies the centripetal force:

Field lines emerge from the north pole, curve around, and enter the south pole. The field is strongest near the poles.

The field forms concentric circles around the wire. The direction is given by the right-hand grip rule: thumb in the direction of conventional current, fingers curl in the direction of $B$.

A long coil of wire carrying current. Inside the solenoid the field is uniform and parallel to the axis (like a bar magnet's interior). Outside, the field resembles that of a bar magnet, with one end acting as north and the other as south.

State the magnitude and direction of the magnetic force on a charged particle moving perpendicular to a magnetic field. [2 marks]

A proton travels at $2.0 \times 10^6$ m s$^{-1}$ perpendicular to a $0.40$ T field. Calculate (a) the force on the proton, and (b) the radius of its circular path. [4 marks]

Refer to the Synchrotron dipole magnets. (a) Calculate the magnetic force on an electron of momentum $1.6 \times 10^{-18}$ kg m s$^{-1}$ in a $1.3$ T field. (b) Determine the orbit radius.