$A$ coil having $N$ turns carries a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is

$N$ equally spaced charges,each of value $q$,are placed on a circle of radius $R$. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. $A$ bigger Amperian loop $B$ encloses the whole circle,whereas a smaller Amperian loop $A$ encloses a small segment. The difference between enclosed currents,$I_A - I_B$,for the given Amperian loops is

Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown in the figure. $AB$ and $CD$ are lines at $45^\circ$ with the axes,with the origin of the axes at $O$. The magnetic field will be zero on the line:

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?

Which of the following is a vector quantity?

$A$ current-carrying circular loop of radius '$R$' and a current-carrying long straight wire are placed in the same plane. The currents through the circular loop and the long straight wire are '$I_C$' and '$I_w$' respectively. The perpendicular distance between the centre of the circular loop and the wire is '$d$'. The magnetic field at the centre of the loop will be zero when the separation '$d$' is equal to: