Magnetic Field Questions

Two concentric coils each of radius equal to $2\pi \text{ cm}$ are placed at right angles to each other. $3\text{ Ampere}$ and $4\text{ ampere}$ are the currents flowing in each coil respectively. The magnetic induction in Weber/m${}^2$ at the centre of the coils will be (${\mu }_0=4\pi \times 10^{-7}$ W/A-m):

A particle of charge $-16\times 10^{-18}\text{C}$ moving with velocity $10\text{m/s}$ along the $x$ -axis enters a region where a magnetic field of induction $B$ is along the $y$ -axis, and an electric field of magnitude $10^4\text{V/m}$ is along the negative $z$ -axis. If the charged particle continues moving along the $x$ -axis, the magnitude of $B$ is:

The dimension of magnetic field $B$ in M, L, T and C (Coulomb) is given as:

A horizontal power line at height $4\text{m}$ carries $100\text{A}$ current from East to West. The magnetic field directly below it on the ground is (${\mu }_0=4\pi \times 10^{-7}\text{Tm/A}$):

A current loop $ABCD$ is held fixed on the plane of the paper. The arcs $BC$ (radius $=b$) and $DA$ (radius $=a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^{\circ }$. The magnitude of the magnetic field ($B$) due to loop $ABCD$ at the origin ($O$) is:

A charge $Q$ is uniformly distributed over the surface of non-conducting disc of radius $R$. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction $B$ is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by: