$AB$ 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 current carrying rectangular loop PQRS is made of uniform wire. The length $PR = QS =5\,cm$ and $PQ = RS =100\,cm$. If ammeter current reading changes from I to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire RS in the two cases respectively $f_{ PQ }^{ I }: f_{ PQ }^{2 I }$ is :

A rectangular loop carrying a current $i$ is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current $I$ is established in wire as shown in figure, the loop will

A conducting wire bent in the form of a parabola $y^2 = 2x$ carries a current $i = 2 A$ as shown in figure. This wire is placed in a uniform magnetic field $\vec B =  - 4\,\hat k$ $Tesla$. The magnetic force on the wire is (in newton)

Two long straight parallel conductors separated by a distance of $0.5\,m$ carry currents of $5\,A$ and $8\,A$ in the same direction. The force per unit length experienced by each other is

A conductor (shown in the figure) carrying constant current $I$ is kept in the $x-y$ plane in a uniform magnetic field $\vec{B}$. If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement$(s)$ is(are) $Image$

$(A)$ If $\vec{B}$ is along $\hat{z}, F \propto(L+R)$

$(B)$ If $\overrightarrow{ B }$ is along $\hat{ x }, F =0$

$(C)$ If $\vec{B}$ is along $\hat{y}, F \propto(L+R)$

$(D)$ If $\overrightarrow{ B }$ is along $\hat{ z }, F =0$