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 :

Two long and parallel straight wires $A$ and $B$ carrying currents of $8.0\, A$ and $5.0\, A$ in the same direction are separated by a distance of $4.0\, cm$. Estimate the force on a $10\, cm$ section of wire $A$

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 $\hat{ z }, F =0$

The force exerted by a magnetic field on a wire having length $L$ and current $I$ is perpendicular to the wire and given as $\left| F \right| = IL\left| B \right|$ . An experimental plot shows $(\vec F)$ as function of $L$ . The plot is a straight line with a slope $S = \left( {10 \pm 1} \right) \times {10^{ - 5}}\ AT$. The current in the wire is $\left( {15 \pm 1} \right)\ mA$ . The percentage error in $B$ is

A conductor in the form of a right angle $ABC$ with $AB = 3\, cm$ and $BC = 4\, cm$ carries a current of $10\, A$. There is a uniform magnetic field of $5\, T$ perpendicular to the plane of the conductor. The force on the conductor will be......$N$

A conducting bar $PQ$ of length $l$ carrying current $I$ is suspended from a rigid support as shown in figure. A uniform magnetic field $B$ perpendicular to $PQ$ and directed away from the reader (inside the plane) is applied. If the mass of the bar is $M$ the tension in each string is