## Moving charges and magnetism

# Magnetic Force and Motion in a Magnetic Field

- When current is flowing through a conductor only magnetic field is produced around the conductor which is non conservative.
- If charge +q is moving with velocity \tt \overline{V}, making an angle ‘θ’ with the direction of field, force acting on the charge is \tt \overline{F} = q. \left(\overline{V} \times \overline{B}\right) = qVB \sin \theta
- The radius of the circular path when a positive charge is projected perpendicular to the magnetic field is given by \tt r = \frac{mv}{Bq} = \frac{P}{Bq} =\sqrt{ \frac{2m KE}{Bq}} (Since KE = kinetic energy)
- The time period of rotation \tt T = \frac{2 \pi r}{V} = \frac{2 \pi m}{Bq}
- When the particle enters the magnetic field at an angle ‘θ’ with B (θ ≠ 0° θ ≠ 90° and θ ≠ 180°) Then the path followed by the particle will be helical and radius of helix = \tt \frac{mv \sin \theta}{Bq}
- Distance travelled by the particle along magnetic field in one complete rotation or pitch of the helix is \tt P = V \cos \theta T = \frac{2 \pi m V \cos \theta}{Bq}
- When a charged particle enters a region of both electric and magnetic fields the force is called Lorentz force F = Fe + Fm = \tt q [E + (\overline{V} \times \overline{B}]
- Force acting on a current carrying conductor in a magnetic field \tt F = i \left(\overline{l} \times \overline{B}\right) = B i l \sin \theta
- If the conductor is semi-circular then force is F = Bi(2r) sin θ

### View the Topic in this video From 0:31 To 10;06

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

1. Force on a charged particle in a uniform magnetic field

\overrightarrow{F} = q(\overrightarrow{v} \times \overrightarrow{B}) \tt\ or\ F = qvB \sin \theta

2. Radius of circular path is R = \frac{mv}{Bq} = \frac{\sqrt{2 mK}}{qB}

3. Time period of revolution is T = \frac{2 \pi R}{v} = \frac{2 \pi m}{qB}

4. The frequency, v = \frac{1}{T} = \frac{qB}{2 \pi m}

5. The force experienced by a straight conductor of length *l* carrying current *I* when placed in a uniform magnetic field \overrightarrow{B} is \overrightarrow{F} = I(\overrightarrow{l} \times \overrightarrow{B}); *F* = *IlB* sin θ