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Question:

In an experiment electrons are accelerated from rest by applying a voltage of 500V. Calculate the radius of the path if a magnetic field of 100mT is then applied. [Charge of the electron = 1.6 × 10⁻¹⁹C, Mass of the electron = 9.1 × 10⁻³¹kg]

7.5m

7.5 × 10⁻⁷m

7.5 × 10⁻⁸m

7.5 × 10⁻⁶m

Solution:

r = √(2mke/B) = √(2meΔV/eB) = √(2 × 9.1 × 10⁻³¹ × 1.6 × 10⁻¹⁹ × 500) / (100 × 10⁻³)
r = √(9.1 × 0.16 × 10⁻⁴⁴ × 10³) / 10⁻² = √9.1 × 0.16 × 10⁻⁴¹ × 10²
= √14.56 × 10⁻³⁹ = 3.8 × 10⁻¹⁹ = 7.5 × 10⁻⁸m