The Earth's magnetic field at a given point is $0.5 \times 10^{-5} \, Wb/m^2$. This field is to be annulled by the magnetic induction at the center of a circular conducting loop of radius $5.0 \, cm$. The current required to be flown in the loop is nearly......$A$

$A$ current of $5 \; A$ flows through a square loop of side length $\frac{1}{\sqrt{2}} \; m$. The magnitude of the magnetic field $B$ at the centre of the square loop is $p \times 10^{-6} \; T$. Find the value of $p$. [Take $\mu_0 = 4 \pi \times 10^{-7} \; T \cdot m \cdot A^{-1}$].

$A$ long straight wire carrying a current of $30\,A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4}\,T$. The magnetic field is acting parallel to the direction of the current. The magnitude of the resultant magnetic induction in tesla at a point $2.0\,cm$ away from the wire is

$A$ point charge $Q (= 3 \times 10^{-12} \, C)$ rotates uniformly in a vertical circle of radius $R (= 1 \, mm)$. The axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular speed $\omega$,the effective magnetic field at the centre of the circle will be reduced to zero? (Horizontal component of earth's magnetic field is $30 \, \mu T$)

$A$ circular coil carrying current $I$ has a radius $R$ and magnetic field at the centre is $B$. The distance from the centre along the axis of the same coil where the magnetic field will be $\frac{B}{8}$ is

$A$ particle is moving with velocity $\overrightarrow{v} = \hat{i} + 3\hat{j}$ and it produces an electric field at a point given by $\overrightarrow{E} = 2\hat{k}$. It will produce a magnetic field at that point equal to (all quantities are in $SI$ units):