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

$A$ single turn current loop in the shape of a right-angled triangle with sides $5\,cm$,$12\,cm$,and $13\,cm$ carries a current of $2\,A$. The loop is placed in a uniform magnetic field of magnitude $0.75\,T$,whose direction is parallel to the current in the $13\,cm$ side of the loop. The magnitude of the magnetic force on the $5\,cm$ side is $\frac{x}{130}\,N$. The value of $x$ is $..........$

Two long straight parallel wires,carrying (adjustable) current $I_1$ and $I_2$,are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other,the graph showing the dependence of $F$ on the product $I_1 I_2$ would be

$AB$ 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 $i$. If the conductor is in equilibrium,find the relation between the given parameters.

$A$ straight wire $AB$ of mass $40\,g$ and length $50\,cm$ is suspended by a pair of flexible leads in a uniform magnetic field of magnitude $0.40\,T$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........$A$. (Take $g=10\,ms^{-2}$).

$A$ straight wire of length $2 \ m$ carries a current of $10 \ A$. If this wire is placed in a uniform magnetic field of $0.15 \ T$ making an angle of $45^{\circ}$ with the magnetic field, the applied force on the wire will be