A charged particle q enters a region of uniform magnetic field B (out of page) and is deflected distance d after travelling a horizontal distance a. The magnitude of the momentum of the particle is

Question

A charged particle q enters a region of uniform magnetic field B (out of page) and is deflected distance d after travelling a horizontal distance a. The magnitude of the momentum of the particle is, q B 2 a 2 d + d, q B 2, Zero, 2 q B

MARKS App · Accepted Answer

From the figure given below we have, A B = a 2 + d 2 = h A B = a 2 + d 2 = h In Δ O A D , c o s θ = h 2 R In Δ A C B , s i n π 2 - θ = d h ⇒ h 2 R = d h ⇒ h 2 = 2 R d ⇒ a 2 + d 2 = 2 R d ⇒ R = a 2 2 d + d 2 ∴ Momentum, P = m v = q B R = q B 2 a 2 d + d ∵ R = m v q B

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