The magnetic field at the centre of a circular coil of radius $r$ carrying current $I$ is $B_1$. The field at the centre of another coil of radius $2r$ carrying the same current $I$ is $B_2$. The ratio $\frac{B_1}{B_2}$ is

The magnetic field due to a current-carrying loop of radius $3 \text{ cm}$ at a point on its axis at a distance of $4 \text{ cm}$ from its centre is $54 \mu\text{T}$. Then,the value of the magnetic field at the centre of the loop is: (in $\mu\text{T}$)

Figures $A$ and $B$ show two long straight wires of circular cross-section (radii $a$ and $b$ with $a < b$),each carrying a current $I$ which is uniformly distributed across the cross-section. The magnitude of the magnetic field $B$ varies with radial distance $r$ from the axis. Which of the following graphs correctly represents the variation of $B$ with $r$ for both wires?

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1 = +10 \text{ A}, I_2 = -13 \text{ A}, I_3 = +10 \text{ A}, I_4 = +7 \text{ A}, I_5 = -12 \text{ A}$ and $I_6 = +18 \text{ A}$. The magnetic induction at a perpendicular distance of $10 \text{ cm}$ from the cable is (Given: $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$) (in $\mu\text{T}$)

$A$ current carrying circular coil of radius $R$ has a point $P$ situated on its axis at a distance $x$ from its centre $O$ of the coil. The magnetic induction at point $P$ is $\left(\frac{1}{8}\right)^{\text{th}}$ of the magnetic field at its centre $O$. The value of $x$ is

In the hydrogen atom,the electron is making $6.6 \times 10^{15} \, r.p.s.$ If the radius of the orbit is $0.53 \times 10^{-10} \, m,$ then the magnetic field produced at the centre of the orbit is (in $Tesla$):