A rigid wire consists of a quarter-circular portion of a circle of radius $R$ and two straight sections (figure). The wire is partially immersed in a perpendicular magnetic field $B$ as shown in the figure. Find the magnetic force on the wire if it carries a current $\mathrm{i}$.

 

Figure shows a part of an electric circuit. The wires $\mathrm{AB}, \mathrm{CD}$ and $\mathrm{EF}$ are very long and have identical resistances. The separation between the neighboring wires is $2 \mathrm{cm}$. The wires $\mathrm{AE}$ and $\mathrm{BF}$ have negligible resistance and the ammeter reads $60 \mathrm{A}$. Calculate the magnetic force per unit length on $\mathrm{AB}$ and $\mathrm{CD}$.

A straight wire of length $l$ can slide on two parallel plastic rails kept in a horizontal plane with a separation $d$. The coefficient of friction between the wire and the rails is $\mu .$ If the wire carries a current $i$, what minimum magnetic field should exist in the space in order to slide the wire on the rails.

$\left(\mathrm{a}\right)$ A circular loop of radius $a$, carrying a current $i$, is placed in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field (figure). The strength of the magnetic field at the periphery of the loop is $B$. Find the magnetic force on the wire.

$\left(\mathrm{b}\right)$ A hypothetical magnetic field existing in a region is given by $\stackrel{\rightharpoonup }{B}=B_0{\stackrel{\rightharpoonup }{e}}_r$, where ${\stackrel{\rightharpoonup }{e}}_r$ denotes the unit vector along the radial direction of a point relative to the origin and $B_0=$constant. A circular loop of radius $a$, carrying a current $i$, is placed with its plane parallel to the $X-Y$ plane and the centre at $\left(0, 0, \mathrm{a}\right)$. Find the magnitude of the magnetic force acting on the loop.