Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. A point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

A solenoid of length 2 m carries a current of 20 A . The diameter of the solenoid is 3 cm . If the magnetic field inside the solenoid is 20 mT , then the length of wire forming the solenoid is (assume, $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )

Two similar coils which are separated by 2 m having radius of 1 m and number of turns 80 have a common axis. Calculate the strength of magnetic field at a point midway between them on their common axis when a current is 0.2 A .

A particle of mass $m$ and charge $Q$ moving with a speed $v$ in a circular path of radius $R$ has magnetic moment $\mu$. If the mass of the particle is doubled and maintains the same speed while revolving in the same circular path, then the magnetic moment will be