A rectangular coil has $100$ turns each of area $50 {\mathrm{cm}}^2$. It is capable of rotation about an axis joining the mid points of two opposite sides. When a current of $5 \mathrm{A}$ is passed through it while its plane is at right angles to a uniform magnetic field, it experiences a torque of $5 \mathrm{N} \mathrm{m}$. The magnetic field will be

A rectangular coil of $100$ turns has length $5 \mathrm{cm}$ and breadth $2 \mathrm{cm}$. It is suspended in radial magnetic field of induction $0.1 \mathrm{Wb} {\mathrm{m}}^{-2}$. If a current of $100 \mu \mathrm{A}$ is passed through the coil, then the torque acting on the coil is

A rectangular coil of $500$ turns with an average area per turn $4.00 {\mathrm{cm}}^2$ carries a current of $0.2 \mathrm{A}$. The coil is placed at an angle of $60°$ with the direction of magnetic induction of ${10}^{-3} \mathrm{Wb} {\mathrm{m}}^{-2}$. The torque acting on the coil is

A $200$ turn rectangular coil measuring $0.02 \mathrm{m}\times 0.08 \mathrm{m}$ of an ammeter is in a magnetic field of induction $0.2 \mathrm{tesla}$. The torsional constant of the suspension fibre is $5\times {10}^{-7 }\mathrm{N} \mathrm{m} {\mathrm{degree}}^{-1}$. Maximum reading of the ammeter corresponds to a deflection of the coil through $45°$. If the magnetic field is radial, then the maximum current that can be measured with this ammeter is

A rectangular coil of area $5.0\times {10}^{-4} {\mathrm{m}}^2$ and $40$ turns is pivoted about one of its vertical sides. The coil is in a horizontal field of $80 \mathrm{gauss}$. If a current of $0.20 \mathrm{mA}$ produces an angular deflection of ${20}^{°}$ then the torsional constant of the hair spring connected to the coil is (in $\mathrm{N} \mathrm{m} {\mathrm{degree}}^{-1}$)

Torque acting on a coil is $2\times {10}^{-5} \mathrm{N} \mathrm{m}$. If the torque produces angular deflection of $10°$ in the coil, then the torsional rigidity of the suspension fibre (in $\mathrm{N} \mathrm{m}$/$\mathrm{degree}$) connected to coil is

A rectangular coil of a moving coil galvanometer containing $100$ turns and $5 \mathrm{cm}$ long and $3 \mathrm{cm}$ broad is suspended in a radial magnetic field of induction $0.025 \mathrm{Wb} {\mathrm{m}}^{-2}$ by a fibre of torque constant $1.5\times {10}^{-9} \mathrm{N} \mathrm{m}$ per degree. The current for which coil will deflect through an angle of $10°$ is

Two identical coils carrying equal current have a common centre and their planes are at right angles to each other. What is the ratio of magnitudes of the resultant magnetic field and the field due to one coil along its axis?

The deflection of galvanometer falls from $60$ to $30$ when $12 \mathrm{\Omega }$ shunt is connected across it. The galvanometer resistance is