A semicircular ring of radius $R$ carrying current $i$ is placed in a magnetic field of intensity $B$ so that plane of wire is perpendicular to magnetic field as shown. Net force acting on the ring is

Two parallel long wires carry currents $i_1$ and $i_2$ with ${i_1} > {i_2}$. When the currents are in the same direction, the magnetic field midway between the wires is $10\, \mu T$. When the direction of $i_2$ is reversed, it becomes $40 \,\mu T$. the ratio ${i_1}/{i_2}$ is

$AB$ and $CD$ are smooth parallel rails, separated by a distance $l$, and inclined to the horizontal at an angle $\theta$ . $A$ uniform magnetic field of magnitude $B$, directed vertically upwards, exists in the region. $EF$ is a conductor of mass $m$, carrying a current $i$. For $EF$ to be in equilibrium,

A winding wire which is used to frame a solenoid can bear a maximum $10\, A$ current. If length of solenoid is $80\,cm$ and it's cross sectional radius is $3\, cm$ then required length of winding wire is $(B = 0.2\,T)$

A metallic loop is placed in a magnetic field. If a current is passed through it, then

Currents of a $10\, ampere$ and $2\, ampere$ are passed through two parallel thin wires $A$ and $B$ respectively in opposite directions. Wire $A$ is infinitely long and the length of the wire $B$ is $2\, m$. The force acting on the conductor $B$, which is situated at $10\, cm$ distance from $A$ will be