Question

A beam of electron passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move

• A. in a circular orbit
• B. along a parabolic path
• C. along a straight line
• D. in an elliptical orbit.

Answer 1

The Correct Option is A

To understand why the electrons move in a circular orbit when the electric field is switched off, and the same magnetic field is maintained, we need to delve into the physics of charged particles in electromagnetic fields.

Initially, the electrons are moving undeflected through mutually perpendicular electric and magnetic fields. This indicates that the force due to the magnetic field is exactly balanced by the force due to the electric field, allowing the electrons to pass straight through.

• If only the electric field acts, the force on the electrons would be due to the electric field: F_{\text{electric}} = eE where e is the charge of the electron and E is the electric field strength.
• Similarly, the magnetic force acting on an electron moving with velocity v in a magnetic field B is given by F_{\text{magnetic}} = evB \sin \theta, where \theta is the angle between the velocity vector and the magnetic field. Since the fields are perpendicular and the electrons pass undeflected, \theta = 90^\circ, hence \sin \theta = 1.

When the electric field is turned off, only the magnetic field exerts a force on the moving electrons. This magnetic force acts as a centripetal force, causing the electrons to move in a circular path.

• The radius of the circular path can be calculated using the balance of the centripetal force and the magnetic force: F_{\text{magnetic}} = m \frac{v^2}{r}, where r is the radius of the circular path, and m is the mass of the electron.
• Rearranging gives: r = \frac{mv}{eB}.

Therefore, in the absence of the electric field, the electrons will move in a circular orbit due to the magnetic field.

Conclusion: When the electric field is switched off, the electrons move in a circular orbit due to the centripetal force provided by the magnetic field. Hence, the correct answer is \text{"in a circular orbit"}.