An electron accelerated through a potential difference V passes through a uniform transverse magnetic field and feels magnetic force F. When the accelerating potential is increased to 2V, the force becomes 2^(1/n)F. Find n.
Physics · Mixed Chapter
JEE Mains

Question

An electron accelerated through a potential difference V passes through a uniform transverse magnetic field and feels magnetic force F. When the accelerating potential is increased to 2V, the force becomes 2^(1/n)F. Find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Electron speed after acceleration: The electrical work becomes kinetic energy: eV = ½mv² ⇒ v = √(2eV/m). Thus v ∝ √V, with e and m unchanged. Step 2 — Magnetic force: For motion perpendicular to uniform magnetic field B, F = evB. Hence F ∝ v ∝ √V. Step 3 — Double the voltage: F(new)/F(old) = √(2V/V) = √2 = 2¹ᐟ². The source writes F(new) = 2¹ᐟⁿF(old), so 1/n = 1/2. Answer: n = 2.