$20$ Figure $6\mathrm{.}22$ shows a current balance in which a loop of wire carrying a current of $3\mathrm{.}6A$ is balanced in the uniform field of a solenoid of field strength $0\mathrm{.}20T.$ The end of the loop $BC$ has a length of $3\mathrm{.}0cm,$ while the length of side $AB$ is $12,0cm.$

FIGURE $6\mathrm{.}22$ A current balance

a Find the magnitude and direction of the magnetic force on side:

i BC of the loop.

ii $CD$ of the loop.

b What length of string of mass $6\mathrm{.}5g{m}^{-1}$ must be placed on the end $xY$ of the loop to restore equilibrium?