Force on moving charge in magnetic and electric fields

An electron (mass \(9\times10^{-31}\) kg and charge \(1.6\times10^{-19}\)C) moving with speed \(c/100\) (\(c\) = speed of light) is injected into a magnetic field \(\vec B\) of magnitude \(9\times10^{-4}\) T perpendicular to its direction of motion. We wish to apply an uniform electric field \(\vec E\) together with the magnetic field so that the electron does not deflect from its path. Then (speed of light \(c = 3\times10^{8}\) ms\(^{-1}\))

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of \(10^5\) m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

In the product

\(\vec{F} = q(\vec{v}\times\vec{B}) = q\,\vec{v}\times(B\hat{i}+B\hat{j}+B_0\hat{k})\)

For q = 1 and \(\vec{v} = 2\hat{i}+4\hat{j}+6\hat{k}\) and \(\vec{F} = 4\hat{i}-20\hat{j}+12\hat{k}\)

What will be the complete expression for \(\vec{B}\) ?

Ionized hydrogen atoms and \(\alpha\)-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths \(r_H : r_\alpha\) will be :

An electron is moving in a circular path under the influence of a transverse magnetic field of \(3.57\times10^{-2}\) T. If the value of \(e/m\) is \(1.76\times10^{11}\) C/kg, the frequency of revolution of the electron is