A teacher wants the magnetic field inside a laboratory solenoid to be exactly four…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A teacher wants the magnetic field inside a laboratory solenoid to be exactly four times the magnetic field produced at the centre of a single-turn circular loop of radius r. Both the solenoid and the loop will be supplied with the same current I. The solenoid has N turns wound uniformly over length ℓ.
(i) Derive an expression for the ratio of the magnetic field at the centre of the loop to the magnetic field inside the solenoid in terms of N, ℓ and r.
(ii) Using the condition that the solenoid field is four times the loop field, obtain a relationship between N, ℓ and r.
(iii) If r=6.0cm and the solenoid available is 30cm long, determine the number of turns that must be wound on the solenoid so that the requirement is met.