An electron moves at a speed of 1000 m/s perpendicular to the direction of a uniform magnetic field of 0.5 T. What is the radius of the electron's circular orbit in units of nanometers (1 m

11.4 nm

Explanation:

The magnetic force drives the circular motion of the electron.

Magnetic force on a charge, q, moving with velocity, v, in a magnetic field, B, moving at angle θ to the field is given by

F = qvB sin θ⁻⁰¹²³⁴⁵⁶⁷⁸⁹

q = charge on an electron = - 1.6 × 10⁻¹⁹ C

v = velocity of the electron = 1000 m/s

B = 0.5 T

Sin θ = sin 90° = 1

F = 1.6 × 10⁻¹⁹ × 1000 × 0.5 = 8.0 × 10⁻¹⁷ N

This force drives the circular motion

F = mv²/r

m = mass of an electron = 9.11 × 10⁻³¹ kg

v = 1000 m/s, r = radius of orbit = ?

8 × 10⁻¹⁷ = (9.11 × 10⁻³¹ × 1000²)/r

r = (9.11 × 10⁻³¹ × 1000²)/(8 × 10⁻¹⁷) = 1.14 × 10⁻⁸ m = 11.4 nm

Explanation:

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find the sum of the two horizontal vectors and the sum of the two vertical vectors

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