Two long parallel wires carry equal current $$i$$ flowing in the same directions are at a distance $$4 d$$ apart. The magnetic field $$B$$ at a point $$P$$ lying on the perpendicular line joining the wires and at a distance $$x$$ from the mid-point is

In a cathode ray tube, a potential difference of 3000 volts is maintained between the deflector plates whose separation is $$2 \mathrm{~cm}$$. A magnetic field of $$2.5 \times 10^{-3} \mathrm{~Wb} / \mathrm{m}^2$$ at right angles to electric field gives no deflection of the electron beam, which received an initial acceleration by a potential difference of $$10000 \mathrm{~V}$$. Calculate $$(\mathrm{e} / \mathrm{m})$$ of an electron.

A stream of electrons is projected horizontally to the right. A straight conductor carrying, a current is supported parallel to the electron stream and above it. If the current in the conductor is from left to right, what will be the effect on the electron stream?

A coil of 100 turns and area $$2 \times 10^{-2} \mathrm{~m}^2$$ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of $$5 \mathrm{~A}$$. When the coil is held with its plane in North-South direction, it experiences a couple of $$0.33 \mathrm{~N}-\mathrm{m}$$. When the plane is East-West, the corresponding couple is $$0.4 \mathrm{~N}-\mathrm{m}$$. The value of magnetic induction is [Neglect earth's magnetic field]