A circular coil of radius $$R$$ is carrying a current $$I_1$$ in anti-clockwise sense. A long straight wire is carrying current $$I_2$$ in the negative direction of $$X$$-axis. Both are placed in the same plane and the distance between centre of coil and straight wire is $$d$$. The magnetic field at the centre of coil will be zero for the value of $$d$$ equal to

A circular coil of radius $$R$$ has a resistance of $$40 \Omega$$. Figure shows two points $$P$$ and $$Q$$ on the circumference separated by a distance $$\frac{\pi R}{2}$$ which are connected to a 16 V battery with internal resistance of $$0.5 \Omega$$. What is the value of current $$I$$ flowing through the circuit?

An $$\alpha$$-particle of energy 10 eV is moving in a circular path in uniform magnetic field. The energy of proton moving in the same path and same magnetic field will be [mass of $$\alpha$$-particle $$=4$$ times mass of proton]

In communication system, a repeater is used to extend the range to transmission. It is the combination of