The magnetic force acting on charged particle of charge $2\,\mu C$ in magnetic field of $2\, T$ acting in $y-$ direction , when the particle velocity is $\left( {2\hat i + 3\hat j} \right) \times {10^6}\,m{s^{ - 1}}$ is

Give expression for the force on a current carrying conductor in a magnetic field.

A proton is projected with a velocity $10^7\, m/s$, at right angles to a uniform magnetic field of induction $100\, mT$. The time (in second) taken by the proton to traverse $90^o$ arc is  $(m_p = 1.65\times10^{-27}\, kg$ and $q_p = 1.6\times10^{-19}\, C)$

An electron enters a chamber in which a uniform magnetic field is present as shown below.  An electric field of appropriate magnitude is also applied, so that the electron travels undeviated without any change in its speed through the chamber. We are ignoring gravity. Then, the direction of the electric field is

A proton and an electron both moving with the same velocity $v$ enter into a region of magnetic field directed perpendicular to the velocity of the particles. They will now move in circular orbits such that

A long solenoid has $100\,turns/m$ and carries current $i.$ An electron moves with in the solenoid in a circle of radius $2·30\,cm$ perpendicular to the solenoid axis. The speed of the electron is $0·046\,c$ ($c =$ speed of light). Find the current $i$ in the solenoid (approximate).....$A$