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

What is the magnitude of magnetic force per unit length (in $N \;m^{-1}$) on a wire carrying a current of $8 \;A$ and making an angle of $30^{\circ}$ with the direction of a uniform magnetic field of $0.15 \;T$?

$A$ straight rod of mass $m$ and length $L$ is suspended from two identical springs as shown in the figure. The springs are stretched by a distance of $x_0$ due to the weight of the rod. The circuit has a total resistance $R$. When a magnetic field perpendicular to the plane of the paper is switched on,the springs are observed to extend further by the same distance $x_0$. The magnetic field strength is:

If a straight current-carrying wire of linear density $0.12 \ kg \ m^{-1}$ is suspended in mid-air by a uniform horizontal magnetic field of $0.5 \ T$ normal to the length of the wire,then the current through the wire is (Acceleration due to gravity $= 10 \ m \ s^{-2}$; Neglect earth's magnetic field) (in $A$)

$P, Q$ and $R$ are long parallel straight wires in air,carrying currents $20 \ A, 40 \ A$ and $60 \ A$ as shown in the figure. What is the direction of the resultant force on $Q$?

$A$ uniform magnetic field of $1.5\; T$ exists in a cylindrical region of radius $10.0\; cm$,its direction parallel to the axis along east to west. $A$ wire carrying current of $7.0\; A$ in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
$(a)$ the wire intersects the axis,
$(b)$ the wire is turned from $N-S$ to northeast-northwest direction,
$(c)$ the wire in the $N-S$ direction is lowered from the axis by a distance of $6.0 \;cm?$