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
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Four wires, each of length $2.0\,m$, are bent into four loops $P,\,Q,\,R$ and $S$ and then suspended in a uniform magnetic field. If the same current is passed in each, then the torque will be maximum on the loop
A uniform conducting wire $A B C$ has a mass of $10 \,g$. A current of $2 \,A$ flows through it. The wire is kept in a uniform magnetic field $B=2 T$. The acceleration of the wire will be ............. $ms ^{-2}$
A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. It the electric field is switched off, and the same magnetic field is maintained, the electrons move
A circular current carrying coil has a radius $R$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}^{th}$ to its value at the centre of the coil, is
An electron with energy $880 \,eV$ enters a uniform magnetic field of induction $2.5 \times 10^{-3}\,T$. The radius of path of the circle will approximately be :
Two circular coils $1$ and $2$ are made from the same wire but the radius of the $1^{st}$ coil is twice that of the $2^{nd}$ coil. What is the ratio of potential difference in volts should be applied across them so that the magnetic field at their centres is the same?
At $t = 0$ a charge $q$ is at the origin and moving in the $y-$ direction with velocity $\overrightarrow v = v\,\hat j .$ The charge moves in a magnetic field that is for $y > 0$ out of page and given by $B_1 \hat z$ and for $y < 0$ into the page and given $-B_2 \hat z .$ The charge's subsequent trajectory is shown in the sketch. From this information, we can deduce that
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