Question

Two particles of masses m₁ and m₂ having charges q₁ and q₂ respectively are projected with the same velocity in a region of uniform magnetic field `vec B` pointing vertically upward. If they describe circular paths as shown in the figure, one may conclude that:

पर्याय

• `m_1/m_2 > q_1/q_2`

• `m_1/m_2 > q_2/q_1`

• `m_1/m_2 < q_1/q_2`

• `m_1/m_2 < q_2/q_1`

Answer 1

`bb(m_1/m_2 < q_1/q_2)`

Explanation:

Given that both particles have the same velocity v and are in the same magnetic field B.

Therefore, r ∝ `m/q`

The radius of the circular path is given by:

r = `(mv)/(qB)`

From the figure provided in the question, we can see that the radius of path 2 is greater than the radius of path 1.

r₂ > r₁

Substituting the formula for radius:

`(m_2 v)/(q_2 B) > (m_1 v)/(q_1 B)`

Cancelling v and B from both sides:

`m_2/q_2 > m_1/q_1`

Rearranging the terms to match the options:

`m_1/m_2 < q_1/q_2`