Biot-Savart Law — Prelims Questions

A current $I$ flows through a long straight wire. The magnetic field produced at a perpendicular distance $r$ from the wire is $B$. If the current is doubled to $2I$ and the distance is halved to $r/2$, what will be the new magnetic field strength?

A circular coil of radius $R$ carries a current $I$. The magnetic field at its center is $B_c$. What is the magnetic field on the axis of the coil at a distance $x = R$ from its center?

According to the Biot-Savart Law, the magnetic field $dvec{B}$ due to a current element $I dvec{l}$ at a distance $vec{r}$ from it is proportional to:

A current $I$ flows in a wire bent into the shape of a regular hexagon of side length $a$. What is the magnetic field at the center of the hexagon?

Two concentric circular coils, one of radius $R_1$ and the other of radius $R_2$ ($R_2 > R_1$), carry currents $I_1$ and $I_2$ respectively. If the currents flow in opposite directions, what is the net magnetic field at the common center?

A current $I$ flows along the positive x-axis. What is the direction of the magnetic field at a point $P(0, y, 0)$ where $y > 0$?