
A proton enters in a uniform magnetic field of 2.0mT at an angle $60^{\circ}$ with the magnetic field with speed 10m/s. Find the pitch of the path.
Answer
162.9k+ views
Hint: When a charged particle goes in a region of magnetic field, two different forces act on it. First one is due to the magnetic field and the other force is centripetal force. The velocity of a particle is constant in the direction parallel to the magnetic field and the motion is accelerating in the direction perpendicular to the magnetic field. We will find the expression for velocity, time period and pitch of the helical path described by the particle.
Formula used:
Magnetic force $P = \dfrac{{2\pi m}}{{qB}}{v_0}$
Complete answer:
Suppose that a charged particle of mass m moves in a circular orbit of radius r, with a constant speed v.
when a charge particle enters in a uniform magnetic field at an angle with some velocity, path of charge must be helix because perpendicular component of velocity creates circular motion whereas parallel component of velocity creates linear motion.
Now the pitch of the helical path is the horizontal distance between two consecutive circles.
i.e., pitch of path = parallel component of velocity × time period
$ = ({v_0}\cos \theta )T$
$ \Rightarrow P = ({v_0}\cos \theta )\dfrac{{2\pi m}}{{qB}}$
$ \Rightarrow P = 10 \times \cos {60^ \circ } \times (\dfrac{{2\pi \times 1.6 \times {{10}^{ - 27}}}}{{1.6 \times {{10}^{ - 19}} \times 2 \times {{10}^{ - 3}}}})$
$ \Rightarrow P = 50\pi \mu m$
Therefore, the pitch is $50~{\pi}{\mu}~m$.
Note: Motion of charged particles is accelerating, in circular motion, in the direction perpendicular to the magnetic field. But, in the direction parallel to the magnetic field, the particle moves with a fixed speed because the magnetic field applies force only in the direction perpendicular to it. Thus, the force can’t do work on the particle, meaning that there is no change in its kinetic energy and therefore, the particle moves with a fixed speed in the direction parallel to the magnetic field.
Formula used:
Magnetic force $P = \dfrac{{2\pi m}}{{qB}}{v_0}$
Complete answer:
Suppose that a charged particle of mass m moves in a circular orbit of radius r, with a constant speed v.
when a charge particle enters in a uniform magnetic field at an angle with some velocity, path of charge must be helix because perpendicular component of velocity creates circular motion whereas parallel component of velocity creates linear motion.
Now the pitch of the helical path is the horizontal distance between two consecutive circles.
i.e., pitch of path = parallel component of velocity × time period
$ = ({v_0}\cos \theta )T$
$ \Rightarrow P = ({v_0}\cos \theta )\dfrac{{2\pi m}}{{qB}}$
$ \Rightarrow P = 10 \times \cos {60^ \circ } \times (\dfrac{{2\pi \times 1.6 \times {{10}^{ - 27}}}}{{1.6 \times {{10}^{ - 19}} \times 2 \times {{10}^{ - 3}}}})$
$ \Rightarrow P = 50\pi \mu m$
Therefore, the pitch is $50~{\pi}{\mu}~m$.
Note: Motion of charged particles is accelerating, in circular motion, in the direction perpendicular to the magnetic field. But, in the direction parallel to the magnetic field, the particle moves with a fixed speed because the magnetic field applies force only in the direction perpendicular to it. Thus, the force can’t do work on the particle, meaning that there is no change in its kinetic energy and therefore, the particle moves with a fixed speed in the direction parallel to the magnetic field.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
Degree of Dissociation and Its Formula With Solved Example for JEE

Charging and Discharging of Capacitor

Instantaneous Velocity - Formula based Examples for JEE

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

In which of the following forms the energy is stored class 12 physics JEE_Main

JEE Main Chemistry Question Paper with Answer Keys and Solutions

Other Pages
Three mediums of refractive indices mu 1mu 0 and mu class 12 physics JEE_Main

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks

NEET Marks vs Rank 2024|How to Calculate?
