A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through $60°$ . The torque required to maintain the needle in this position will be
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A charged particle with specific charge $S$ moves undeflected through a region of space containing mutually perpendicular uniform electric and magnetic fields $E$ and $B$ . When electric field is switched off, the particle will move in a circular path of radius
A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) T$. If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) m / s ^{2}$, then the value of $\alpha$ will be.
A coaxial cable consists of an inner wire of radius $'a'$ surrounded by an outer shell of inner and outer radii ' ${b}$ ' and '$c$' respectively. The inner wire carries an electric current is, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance ${x}$ from the axis when $(i)$ ${x}<{a}$ and $(ii)$ ${a}<{x}<{b}$ ?
An electron having charge $1.6 \times {10^{ - 19}}\,C$ and mass $9 \times {10^{ - 31}}\,kg$ is moving with $4 \times {10^6}\,m{s^{ - 1}}$ speed in a magnetic field $2 \times {10^{ - 1}}\,tesla$ in a circular orbit. The force acting on electron and the radius of the circular orbit will be
$A$ galvanometer may be converted into ammeter or voltmeter. In which of the following cases the resistance of the device will be the largest ? (Asssume maximum range of galvanometer $= 1\, mA$)