Paper 3 Magnetic Force Drills

Q1 Circular Motion of Ions

A singly charged positive ion of mass $3.3\times 10^{-26}\mathrm{kg}$ moves at $2.5\times 10^5\mathrm{m}{\mathrm{s}}^{-1}$ perpendicular to a uniform magnetic field. Its circular path radius is $0.18\mathrm{m}$.

1. Show that the magnetic flux density is about $0.29\mathrm{T}$. [3]
2. Explain the direction of the force at any instant. [2]
3. State how the radius changes if the ion speed is doubled. [2]

Q2 Parallel Currents

Two long parallel wires are separated by $4.0\mathrm{cm}$ and carry currents $8.0\mathrm{A}$ and $5.0\mathrm{A}$ in the same direction.

1. State whether the force is attractive or repulsive. [1]
2. Calculate the force per unit length using $F/L={\mu }_0{I}_1{I}_2/(2\pi d)$, where ${\mu }_0=4\pi \times 10^{-7}\mathrm{N}{\mathrm{A}}^{-2}$. [3]
3. Explain the force using field from one wire acting on the current in the other. [3]