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Force On A Moving Charge In Magnetic Field - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Force on a moving charge in magnetic field is considered one of the most asked concept.

  • 48 Questions around this concept.

Solve by difficulty

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then

A particle of mass M and  charge  Q moving with velocity \vec{v} describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B . The work done by the field when the particle completes one full circle is

A negative test charge is moving near a long straight wire carrying a current.  The force acting on the test charge is parallel to the direction of the current.  The motion of the charge is :

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

At a specific instant, the emission of the radioactive compound is deflected in a magnetic field. The compound can emit

(i)\; electrons  

(ii)\; protons

(iii)\; He^{2+}

(iv)\; neutrons

The emission at the instant can be

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Concepts Covered - 1

Force on a moving charge in magnetic field

Force on a moving charge in magnetic field: 

The magnetic force  on a free moving charge is perpendicular to both the velocity of the charge and the magnetic field with direction given by the right hand rule. The force is given by the charge times the vector product  of velocity and magnetic field.

The force is always perpendicular to both the magnetic field and velocity.

\begin{aligned} F &=q v B \sin \theta \\ F &=q v B \text { if } \theta=90 \end{aligned}

If the velocity is perpendicular to the magnetic field then the force is given by the simple product :

Force  = charge  x  velocity  x  B-field 

Right hand rule:

Magnetic force is as important as the electrostatic or Coulomb force. Yet the magnetic force is more complex, in both the number of factors that affects it and in its direction, than the relatively simple Coulomb force. The magnitude of the magnetic force F on a charge q moving at a speed v in a magnetic field of strength B is given by

qvB sin θ,

where θ is the angle between the directions of v and B. This force is often called the Lorentz force. In fact, this is how we define the magnetic field strength B—in terms of the force on a charged particle moving in a magnetic field. The SI unit for magnetic field strength B is called the tesla (T).  Therefore magnetic field strength is given as :   

 B=\frac{F}{q v \sin \theta}

The unit of tesla is :

1 \mathrm{T}=\frac{1 \mathrm{N}}{\mathrm{C} \cdot \mathrm{m} / \mathrm{s}}=\frac{1 \mathrm{N}}{\mathrm{A} \cdot \mathrm{m}}

  • The direction of the force on a moving charge is given by right hand rule . Point the thumb of the right hand in the direction of v, the fingers in the direction of B, and a perpendicular to the palm points in the direction of F.
  • The force is perpendicular to the plane formed by v and B. Since the force is zero if v is parallel to B, charged particles often follow magnetic field lines rather than cross them.

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Force on a moving charge in magnetic field

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