A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. The current through circular loop and long straight wire are ' $I_c$ ' and ' $\mathrm{I}_{\mathrm{w}}$ ' respectively. The perpendicular distance between centre of the circular loop and wire is ' d '. The magnetic field at the centre of the loop will be zero when separation ' $d$ ' is equal to

Magnetic field at the centre of a circular loop of area ' $A$ ' is ' $B$ '. The magnetic moment of the loop will be

A boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5} \mathrm{~N} / \mathrm{Am}$ due north and horizontal. The boat carries a vertical conducting rod 2 m long. If the speed of the boat is $2.00 \mathrm{~m} / \mathrm{s}$, the magnitude of the induced e.m.f. in the rod is

The magnetic flux near the axis and inside the air core solenoid of length 80 cm carrying current ' I ' is $1.57 \times 10^{-6} \mathrm{~Wb}$. Its magnetic moment will be [cross-sectional area of a solenoid is very small as compared to its length, $\mu_0=4 \pi \times 10^{-7}$ SI unit $](\pi=3.14)$