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An $\alpha - $ particle travels in a circular path of radius $0.45\, m$ in a magnetic field $B = 1.2\,Wb/{m^2}$ with a speed of $2.6 \times {10^7}\,m/\sec $. The period of revolution of the $\alpha - $ particle is
An electron (mass $= 9 \times 10^{-31}\,kg$. Charge $= 1.6 \times 10^{-19}\,C$) whose kinetic energy is $7.2 \times 10^{-18}$ $joule$ is moving in a circular orbit in a magnetic field of $9 \times 10^{-5} \,weber/m^2$. The radius of the orbit is.....$cm$
A proton of mass $1.67\times10^{-27}\, kg$ and charge $1.6\times10^{-19}\, C$ is projected with a speed of $2\times10^6\, m/s$ at an angle of $60^o$ to the $X-$ axis. If a uniform magnetic field of $0.104\, tesla$ is applied along the $Y-$ axis, the path of the proton is
A square loop of side $2\, a ,$ and carrying current I, is kept in $XZ$ plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to the $z-$axis and passing through the point $(0, b, 0),(b>>a)$. The magnitude of the torque on the loop about $z-$axis is given by:
Two coaxial solenoids of different radii carry current $I$ in the same direction. Let $\;{\overrightarrow {\;F} _1}$ be the magnetic force on the inner solenoid due to the outer one and $\;{\overrightarrow {\;F} _2}$ be the magnetic force on the outer solenoid due to the inner one. Then
An electron moves straight inside a charged parallel plate capacitor of uniform charge density. The space between the plates is filled with uniform magnetic field of intensity $B ,$ as shown in the figure, Neglecting effect of gravity, the time of straight line motion of the electron in the capacitor is