An electron moves at speed c/100 perpendicular to a uniform magnetic field of magnitude 9 × 10⁻⁴ T. What orientation and magnitude of a uniform electric field would keep it undeflected? Take c = 3 × 10⁸ m/s.
Options

Question

An electron moves at speed c/100 perpendicular to a uniform magnetic field of magnitude 9 × 10⁻⁴ T. What orientation and magnitude of a uniform electric field would keep it undeflected? Take c = 3 × 10⁸ m/s.

Options

G1 Physics · Accepted Answer

Step 1: The electron remains undeflected only if the electric and magnetic forces cancel: q(E + v × B) = 0. Step 2: Thus E = −v × B, so E is perpendicular to B and to velocity. Step 3: v = c/100 = 3 × 10⁸/100 = 3 × 10⁶ m/s. Step 4: Since v ⟂ B, |E| = vB = (3 × 10⁶)(9 × 10⁻⁴) = 27 × 10² V/m. Final answer: E ⟂ B; |E| = 2.7 × 10³ V/m, Option B.