Question

Two electron beams having velocities in the ratio of 1:2 are separately subjected to regions of magnetic field strength in the ratio of 1:2, respectively. the ratio of the radii of the circular paths they will traverse will be

Answer 1

The ratio of the radii path is 1:2.
Answer

Answer 2

Hey there!

Answer: 1:1

Explanation:

We know that the radius inscribed by the particle will be given by the expression: r = $\frac{mv}{qB}$    { m === Mass                         }

                                 { v === velocity                      }

                                 {q === charge of the particle}

                                 {B === Magnetic files             }

Let the first e- beam inscribe radius r₁ and the second inscribe radius r₂

Hence:

r₁ = mv₁ / qB₁   ----- (1)

r₂ = mv₂ / qB₂ ----- (2)

(1) / (2)

*{ since both the beams are e- , their mass and charge remain the same... they cancel out. This is what remains:}

r₁ / r₂ = v1/v2 x B2/B1

        = 1/2 x 2/1

        = 1/1

                                   ∴  r₁ : r₂  = 1 : 1