Draw the pattern of magnetic field lines through and around a current-carrying circular loop of wire. How would the strength of the magnetic field produced at the centre of the circular loop be affected if: $(i)$ the strength of the current passing through this loop is doubled? $(ii)$ the radius of the loop is reduced to half of the original radius?

(N/A) The pattern of magnetic field lines for a current-carrying circular loop is similar to that of a bar magnet,where the field lines are circular near the wire and become nearly parallel straight lines at the centre of the loop.
$(i)$ The magnetic field strength at the centre is given by $B = \frac{\mu_0 I}{2R}$. Since $B \propto I$,if the current $I$ is doubled,the magnetic field strength $B$ will also be doubled.
$(ii)$ Since $B \propto \frac{1}{R}$,if the radius $R$ is reduced to half $(R' = R/2)$,the new magnetic field strength $B'$ becomes $B' = \frac{\mu_0 I}{2(R/2)} = 2 \times \frac{\mu_0 I}{2R} = 2B$. Thus,the magnetic field strength will be doubled.