Question

A proton is projected with speed v in magnetic field B of magnitude 1 T. The angle between velocity and magnetic field is 600 as shown below. The kinetic energy of a proton is 2 eV (mass of proton = \(1.67\times10^{-27} kg\), e = \(1.6\times10^{-19}\)C). The pitch of the path of the proton is approximately?

• A. 6.28 x 10^-2 m
• B. 6.28 x 10^-4 m
• C. 3.14 x 10^-2 m
• D. 3.14 x 10^-4 m

Answer 1

The Correct Option is B

The correct option is (B) : \(6.28\times10^{-4}\) m
\(R = \frac{mv\, sin60^{\circ}}{qB}\)
\(T-\frac{2\pi m}{qB}\,\,\,\,\,K.E = -\frac{1}{2}mv^2\)
pitch = \(v\,cos\theta\times(\frac{2\pi m}{qB})\,\,\,\,\,\,\,\,\sqrt{\frac{2K}{M}}=v\)
\(\sqrt{\frac{2K}{M}}\times\frac{1}{2}\times\frac{2\pi m}{qB}\)
= \(\frac{\pi}{eB}.\sqrt{2Km}=\frac{3.14}{1.6\times10^{-19}\times1}\times\sqrt{2\times2\times(1.6)^2\times10^{-46}}\)
\(=\frac{3.14}{1.6\times10^{-19}}\times2\times1.6\times10^{-23}\)
\(=6.28\times10^{-4}m\)
 

Answer 2

The force experienced by a charged particle moving in a magnetic field is given by the equation:
F = q v x B
where q is the charge of the particle, v is its velocity, and B is the magnetic field. The direction of the force is perpendicular to both v and B and is given by the right-hand rule.
The magnitude of the force is given by:
|F| = q v B sinθ
where θ is the angle between v and B.
Since the proton is moving perpendicular to the magnetic field, the angle θ is 90 degrees and sinθ is equal to 1. Therefore, the magnitude of the force on the proton is:
|F| = q v B
The force causes the proton to move in a circular path with radius r, given by:
\(|F| = \frac{(m v^2)}{r}\)
where m is the mass of the proton.
Equating the two expressions for |F|, we get:
\(qvB= \frac{(m v^2)}{r}\)
Solving for r, we get:
\(r = \frac{m v}{(q B)}\)
Substituting the given values, we get:
r = \((1.67 x 10^{-27} kg) \frac{\sqrt{2 x 1.6 x 10^{-19} J}} {1.6 x 10^{-19} C x 1 T}\)
r = 6.28 x 10^-4 m
Therefore, the pitch of the path of the proton is approximately 6.28 x 10^-4 m.
Hence, the correct option is (B) 6.28 x 10^-4 m.
Answer. B