A current of $i$ ampere is flowing in an equilateral triangle of side $a$. The magnetic induction at the centroid will be
$\frac{\mu_0 i}{3 \sqrt{3} \pi a}$
$\frac{3 \mu_0 i}{2 \pi a}$
$\frac{5 \sqrt{2} \mu_0 i}{3 \pi a}$
$\frac{9 \mu_0 i}{2 \pi a}$
Assertion : A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.
Reason : Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\overrightarrow B $ in a direction perpendicular to $\overrightarrow B $, will describe circular trajectories of equal radii.
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
The radius of curvature of the path of the charged particle in a uniform magnetic field is directly proportional to
An electron having kinetic energy $T$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic induction $\vec B$ . If kinetic energy is doubled and magnetic induction tripled, the radius will become
A particle having some charge is projected in $x-y$ plane with a speed of $5\ m/s$ in a region having uniform magnetic field along $z-$ axis. Which of the following cannot be the possible value of velocity at any time ?