A single circular turn of wire of radius carries a steady current
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits · Magnetostatics
Electricity, Magnetism and Electromagnetism, Ch The Biot-Savart law and the fields of steady currents
Problem
A single circular turn of wire of radius 8.0cm carries a steady current. The wire has cross-sectional area 0.80mm2 and the current density in it is uniform, of magnitude 2.5×106Am−2. An alpha particle, of charge +2e, passes through the centre of the loop moving in the plane of the loop at 5.0×105ms−1. The wire is thin, the current is steady and gravity is ignored.
((a)) Find the current in the loop.
((b)) Find the magnetic field at the centre of the loop.
((c)) Find the magnitude of the magnetic force on the alpha particle at the centre, and state its direction relative to the particle's velocity.
((d)) At what separation would the Coulomb repulsion between this alpha particle and a single proton have the same magnitude as the force found in part (c)?