Question

An electron accelerated through potential difference \(V\) passes through a uniform transverse magnetic field and experiences a force \(F\). If the accelerating potential is increased to \(2V\), the electron in the same magnetic field will experience a force

• A. \(3F\)
• B. \(F\)
• C. \(\sqrt{2}\,F\)
• D. \(\dfrac{F}{2}\)

Hint:

Magnetic force depends on velocity, and velocity of a charged particle accelerated by a potential varies as \(\sqrt{V}\).

Answer 1

The Correct Option is C

Step 1: Expression for magnetic force.
The magnetic force on a charged particle moving perpendicular to a magnetic field is \[ F = qvB \]

Step 2: Relation between velocity and accelerating potential.
For an electron accelerated through potential \(V\): \[ \frac{1}{2}mv^2 = eV \Rightarrow v \propto \sqrt{V} \]

Step 3: Effect of doubling the potential.
When potential becomes \(2V\): \[ v' = \sqrt{2}\,v \] Hence, \[ F' = qv'B = \sqrt{2}\,F \]