The magnetic field at a distance of $10 \ cm$ from a long straight thin wire carrying a current of $4 \ A$ is (in $\mu T$)

As shown in the figure,two infinitely long,identical wires are bent by $90^{\circ}$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis,while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP = OQ = 4\, cm$,the magnitude of the magnetic field at $O$ is $10^{-4}\, T$,and the two wires carry equal current $i$ (see figure),find the magnitude of the current in each wire and the direction of the magnetic field at $O$. $(\mu_0 = 4\pi \times 10^{-7}\, NA^{-2})$

Two infinitely long parallel wires carry currents of magnitude $I_1$ and $I_2$ and are at a distance $4 \, cm$ apart. The magnitude of the net magnetic field is found to reach a non-zero minimum value between the two wires at a distance of $1 \, cm$ from the first wire. The ratio of the two currents and their mutual direction is

Give two different properties of a current-carrying coil and state Ampere's suggestion.

Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current $I_1$ and $COD$ carries a current $I_2$. The magnetic field at a point lying at a distance $d$ from $O$,in a direction perpendicular to the plane of the wires $AOB$ and $COD$,will be given by

Two circular coils $P$ and $Q$ are made from similar wire,but the radius of $Q$ is twice that of $P$. What should be the value of the potential difference across them so that the magnetic induction at their centres is the same?