A charged particle enters into a uniform magnetic field with velocity vector at an angle of $4 5^{o}$ with the magnetic field. The pitch of the helical path followed by the particle is $p$ . The radius of the helix will be

Question

Verified by Toppr

Answer 1

Pitch of the helix is product of velocity component along the magnetic field and the time period $T$ .

Pitch: $p = \frac{2 π m}{q B} v cos θ = \frac{2 π P cos θ}{q B} = \frac{2 π P cos 4 5 ^{0}}{q B}$
Here $P$ denotes momentum
Radius of the helix $: r = \frac{m v sin θ}{q B} = \frac{m v sin 4 5 ^{0}}{q B} = \frac{P sin 4 5 ^{0}}{q B}$

$∴ p = 2 π r$

$\Rightarrow r = \frac{p}{2 π}$

Answer 2

Pitch of the helix is product of velocity component along the magnetic field and the time period

T

.

Pitch:

p = \frac{2 π m}{q B} v cos θ = \frac{2 π P cos θ}{q B} = \frac{2 π P cos 4 5 ^{0}}{q B}

Here

P

denotes momentum

Radius of the helix

: r = \frac{m v sin θ}{q B} = \frac{m v sin 4 5 ^{0}}{q B} = \frac{P sin 4 5 ^{0}}{q B}

∴ p = 2 π r

\Rightarrow r = \frac{p}{2 π}