Two parallel conductors,each $50 \ m$ long,separated by $0.2 \ m$,experience a force of $1 \ N$. If the current in the first conductor is twice that of the second conductor,what is the current in the second conductor (in $A$)? (Given: $\mu_0 = 4 \pi \times 10^{-7} \ T \cdot m/A$)

Give the uses of electromagnets.

$A$ 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 $6.0 \;cm?$

$A$ wire $X$ of length $50 \; cm$ carrying a current of $2 \; A$ is placed parallel to a long wire $Y$ of length $5 \; m$. The wire $Y$ carries a current of $3 \; A$. The distance between the two wires is $5 \; cm$ and the currents flow in the same direction. The force acting on the wire $X$ due to wire $Y$ is:

$A$ square loop of length $L$ is placed with its edges parallel to the $XY$-axes. The loop carries a current $I$. If the magnetic field in the region varies as $B = B_0 \left(1 + \frac{xy}{L^2}\right) \hat{k}$,then the magnitude of the net force on the loop will be:

The circuit in the figure consists of wires at the top and bottom and identical springs as the left and right sides. The wire at the bottom has a mass of $10 \, g$ and is $5 \, cm$ long. The wire is hanging as shown in the figure. The springs stretch $0.5 \, cm$ under the weight of the wire and the circuit has a total resistance of $12 \, \Omega$. When the lower wire is subjected to a static magnetic field,the springs stretch an additional $0.3 \, cm$. The magnetic field is