An electron (mass = 9 × 10⁻³¹ kg, charge = 1.6 × 10⁻¹⁹C) moving with a velocity of 10⁶m/s enters a magnetic field. If it describes a circle of radius 0.1 m, then strength of magnetic field must be

Concept:

The electron moves in a circular path due to the magnetic force acting as the centripetal force.

Formula Used:

Magnetic force (qvB) = Centripetal force (mv²/r)

Calculation:

We have,

⇒ qvB = mv²/r

⇒ B = (mv)/(qr) ...........(1)

Substituting the given values,

⇒ B = (9 × 10^-31 kg × 10⁶ m/s) / (1.6 × 10^-19 C × 0.1 m)

⇒ B = (9 × 10^-25 kg·m/s) / (1.6 × 10^-20 C·m)

⇒ B = 5.625 × 10^-5 T

Thus, the strength of the magnetic field must be approximately 5.5 × 10^-5 T (option 3).

∴ The correct answer is option 3.