A length of resistance wire is first bent to form a single circular loop of radius

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism

Problem

R

. When a current

I

passes through it, the magnetic field at its centre is

B_1

. The same wire is then rebent so that it forms two identical circular loops joined in series (the same current

I

flows through both), each of radius

r

, and their centres coincide. (i) Express the total length of the wire in terms of

R

. Hence show that after rebending, the radius of each loop is

r = \dfrac{R}{2}

. (ii) Derive an expression for the magnetic field

B_2

at the common centre of the two-loop arrangement in terms of

I

and

r

. (iii) Calculate the ratio

\dfrac{B_2}{B_1}

and hence determine the percentage increase in the magnetic field at the centre after the wire is rebent into two loops.