A charged particle of mass m and charge q is projected perpendicu… — Solution | JEE Physics

MCQEasyJEE 2024Force on Moving Charge

A charged particle of mass $m$ and charge $q$ is projected perpendicular to a magnetic field $B$ with speed $v$ . The pitch of the helical path followed by the particle is:

A
$2\pi mv/qB$
B
$2mv/qB$
C
$2\pi qB/mv$
D
$2qB/\pi mv$

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A charged particle has mass $m$ , charge $q$ , moves in magnetic field $B$ with speed $v$ .

Find: The pitch of the helical path.

The provided solution states that the formula used for the pitch gives:

\text{Pitch} = \frac{2\pi mv}{qB}

Therefore, the correct option is A and the pitch is $\frac{2\pi mv}{qB}$ .

Common mistakes

Using the radius formula instead of the pitch formula is incorrect because radius and pitch describe different parts of helical motion. Use the expression given for pitch, not the circular radius.
Inverting $m$ and $qB$ leads to the wrong option because the pitch must be proportional to $m$ and $v$ and inversely proportional to $qB$ . Keep the dependence in the correct order.

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Answer

Step-by-step solution

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