Force on a Moving Charge

Iron items are attracted to the poles of a bar magnet. One end of the magnet is the north pole, the other one is the south pole. Magnetism is generated by the force created by magnets, thereby further creating fields that cause diverse metallic objects to attract or repel one another. Particles that are electrically charged are the source of this phenomena. The size of the charge, the magnetic field’s strength, and the particle’s velocity all influence the force exerted on the particles that are electrically charged in a magnetic field. As per the laws of magnetism, when two magnets are pulled closely together, like poles repel and unlike poles attract one another.

The Force on a Moving Charge in a Magnetic Field

A charge will experience a force if it moves through a magnetic field at an angle. F = qvB sin θ is the equation where q is the charge, B is a magnetic field, v is the velocity, and θ is the angle between the magnetic field and the velocity directions. A force acts on the motion of charge q, travelling with velocity v in a magnetic field is called the force on a moving charge in a magnetic field.

Magnetic Field 

When a positively charged particle moves through a magnetic field with consistent direction and magnitude, its velocity remains perpendicular. This is because the magnetic force is always perpendicular to the charge’s motion. The magnetic field is, in simple terms, the space around a magnet where the magnetic force is exerted on other magnets.

The magnetic field of a bar magnet is located with the usage of a magnetic compass by taking into consideration the following facts:

• When kept away from the magnet, a compass does not deflect. 
• A magnetic compass deflects as it gets closer to another magnet. The magnetic field is powerful when the lines in the magnetic field in each location are quite close to one another, and is fragile when they are far apart. It is measured in Tesla units.

Magnetic Force on Charged Particles in a Magnetic Field

The magnetic force on a charged particle in a magnetic field is perpendicular to the charge’s velocity and the magnetic field, with the right-hand rule dictating the direction. The charge multiplied by the vector product of velocity and magnetic field equals force.

What technique does one magnet use to put force on another? The solution has to do with the fact that the current, or the passage of charge, is the source of all magnetism. The moving charges exert force on magnetic fields, which impose forces on other magnets with moving charges.

The magnetic pull on a moving charge is among the fundamental forces. The magnetic force is simply as significant as the electrostatic or Coulomb force. However, the magnetic force on a moving charge is more complicated than the relatively basic Coulomb force in terms of the number of things that affect it as well as its direction. In a magnetic field of strength B, the magnetic force F on a charge q travelling at a speed v is given by

F = qvB sin θ

What is the right-hand thumb rule to determine the force on a moving charge?

According to the right-hand rule  (RHR), the magnetic force F is perpendicular to the plane formed by v and B. To identify the direction of the magnetic force on a positive moving charge, point the right hand’s thumb in the direction of v, the fingers in the direction of B, and a perpendicular to the palm in the direction of F, according to RHR. One method to remember this is that there is only one velocity, which is represented by the thumb. The fingers symbolise the many field lines. The force is directed in the direction in which your palm would push. A negative charge’s force is the opposite of a positive charge’s force.

A charged particle can move in a spiral or circular route due to the magnetic force on a moving charge. Cosmic rays are intensely charged particles in space that occasionally come close to the earth. The magnetic field of the earth can drive them into spiral routes. The magnetic force keeps protons in enormous accelerators on a circular course. The charged particles in the magnetic field follow curved pathways, exploited analytically in a mass spectrometer.

Rule of the Right Hand for the Force on a Moving Charge

You can use the right-hand rule for determining the force’s direction (F).

It indicates the devices that depend on generating current by opting to move in a magnetic field.

• Move your index finger along the moving charge or direction of velocity v.
• Rotate the middle finger away from the index finger between points v and B.
• Maintain a perpendicular relationship between your thumb and the plane formed by your fingers.
• Your thumb will point towards the force’s direction if the charge is positive.

Does magnetic force cause circular motion? 

The charged particle is unaffected by the force on a moving charge in a magnetic field since it is always perpendicular to the velocity. The kinetic energy and speed of the particle are thus maintained. This typifies the uniform circular motion (In a vacuum, the magnetic field dominates the motion). The centripetal force, Fc=mv2/r, is provided by the magnetic force. We can observe that F=qvB because sin θ = 1.

We have qvB=mv2/r because the magnetic force F gives the centripetal force Fc.

Solving for r, we will get

r=mv/qB

The Force of Attraction for the Force on a Moving Charge in a Magnetic Field

The force on a moving charge in a magnetic field arises from the motion of electrically charged particles and acts as an attraction or repellent force. The magnetic force exerted on two moving charges by the magnetic field established by the other can be expressed as the magnetic force exerted on their charge by the magnetic field created by the other. 

A motor, a compass, railroad tracks, and magnets that are put on the door of a refrigerator are a few examples of magnetic force. All moving charges create a magnetic field, and the charges that move across its regions experience a force. It can be positive or negative depending on whether the force is repulsive or attractive. The magnetic force is ascertained by the object’s charge, velocity, and magnetic field.

Solved Example:

1. How do you calculate the magnetic force of 50 C charged particles travelling at 3m/s in a 1T magnetic field? Its field has the same direction as the second particle’s travel.

q=50C

v=3m/s

B=1T is the given parameters.

Because the second particle’s route difference is the same as its field’s direction, 0°

F= q v B sinθ = 5031 sin 0°  = 0 is the magnitude  of force.

Conclusion

We have discussed how magnetic fields affect moving charges as well as how to determine the velocity and direction of a field. The fundamental calculations will bring forth the factors on which it affects the direction and the magnitude of external forces.