Question

A cosmic-ray electron moves at perpendicular to earth’s magnetic field at an altitude where the field strength is. what is the radius of the circular path the electron follows?

Answer 1

4.266 m is the radius of the circular path the electron follows.

Given

Speed of electron (v) = 7.5 × 10⁶ m/s

Earth's Magnetic Field (B) = 1 × 10⁻⁵ T

We already know that

Mass of electron (m) = 9.1 × 10⁻³¹ kg

Charge on electron (q) = 1.6 × 10⁻¹⁹ C

According to the formula

Radius of circular path(r) = mass on electron × speed/ Charge × Magnetic field

Radius of circular path(r) = m × v/q × B

Put the values into the formula

r = 9.1 × 10⁻³¹ × 7.5 × 10⁶/ 1.6 × 10⁻¹⁹ × 10⁻⁵

On solving, we get

r = 4.266 m

Hence, 4.266 m is the radius of the circular path the electron follows.

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