$A$ long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $a/2$ and $2a$ is:

Two parallel wires in the plane of the paper are at a distance $X_0$ apart. $A$ point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\frac{X_0}{X_1}=3$, the value of $\frac{R_1}{R_2}$ is:

$A$ non-conducting disc of radius $R$ has a surface charge density which varies with distance from the centre as $\sigma(r) = \sigma_0 \left[1 + \sqrt{\frac{r}{R}}\right]$,where $\sigma_0$ is a constant. The disc rotates about its axis with angular velocity $\omega$. If $B$ is the magnitude of magnetic induction at the centre,then $\frac{B}{\mu_0 \sigma_0 \omega R}$ will be

$A$ current passing through a circular coil of two turns produces a magnetic field $B$ at its centre. The coil is then rewound so as to have four turns and the same current is passed through it. The magnetic field at its centre now is

Which of the following is a vector quantity?

$PQRS$ is a square loop made of a uniform conducting wire. The current enters the loop at $P$ and leaves at $S$. Then the magnetic field will be