Force on a moving charge wire in a uniform magnetic field

Magnetism can be defined as an effect of the magnetic field created by the magnets due to the moving electric charges which result in attracting or repelling other magnets. They can also change the direction of motion of other charged particles. These charges can be gained or lost depending on time and other factors which affect its magnetic field but some materials, for example, iron, acts as a permanent magnet and can remain charged without getting affected by other factors. Other materials like nickel and cobalt will lose their magnetism once the larger magnetic field which is the source of magnetism is removed.

What is a uniform magnetic field?

As we know, magnetism is a force produced by moving electric charges. The force which is acting on the electrically charged particles in a magnetic field depends on the strength of the charge, the velocity at which the particle is moving, and the strength of the magnetic field. Depending upon the direction of magnetic field lines, the magnetic fields are divided into two types, i.e., uniform magnetic fields and non-uniform magnetic fields. In uniform magnetic fields, the strength of the magnetic field remains constant throughout the magnetic field and the direction of the magnetic field lines is parallel to each other. Whereas in a non-uniform magnetic field the magnitude of the magnetic field differs from point to point in the magnetic field and the magnetic field lines are also not parallel to each other.

What is a uniform magnetic field?

A uniform electric field is often formed by two parallel conducting plates with equal and opposite charges, such that the electric lines of force are parallel and equally spaced, and the electric field is constant at all points in the region between the plates. Magnetic force in an equation form can be written as F=Q(V.B) where F stands for the magnetic force exerted on an imaginary particle X, Q denotes charge, V denotes the velocity and B denotes the magnetic field. The magnetic field is created when electrons travel at a high velocity inside a conductor. Every electrical appliance that we use today produces a magnetic field around it as it uses electricity to operate. The magnetic field can often lead to losses in electricity if not taken into account for its activity caused inside a closed-loop circuit.

What is the effect of a magnetic field on a charged wire? 

Electrons are nothing but negatively charged elements of atoms and when these electrons flow freely through a conductor, electricity is generated. Every electrical appliance that we use today has its own electric field, may it be the laptop we use or even a simple LED light produces an electric field due to the movement of electrons within them. Whenever we consider a closed-loop electrical circuit we have to be highly careful about all the parameters that we are using to calculate as sometimes the magnetic field generated by these circuits can even lead to a reversal of the direction of current

Right-hand thumb rule

Since we know that the magnetic field is produced by the current, we can also find out the direction of the uniform magnetic field by the right-hand thumb rule.

When you hold your right hand in the thumbs-up sign, the current will flow in the direction the thumb is pointing, and the magnetic field will be described by the direction of the fingers.

This indicates that the direction of the current is reversed. As we have studied earlier, current always travels from the positive terminal of the battery to the negative. 

A mathematical equation to find the force on a moving charge wire in a uniform magnetic field 

As we have learned before, to find magnetic force F= Q(V.B), 

where q is the charge of the particle, times the velocity of the particle with the magnetic field B.

Here velocity can be rewritten as l/t i.e., the distance vector divided by time.

Applying the same in the equation,

F= Q(1/t * l * B)

Solving this equation we get,

F=Q/t(l*B)

What is Q/t i.e., charge divided by time? The answer is current (I)

F=I(l*B)

Therefore, the force of the magnetic field can be determined by the product of current (I) times distance into a magnetic field.

And to further get the direction of the uniform magnetic field the right-hand thumb rule can be applied as we studied earlier above.

Conclusion

Therefore, in this article, we learned about what is a magnetic field, the difference between the uniform magnetic field and non-uniform magnetic field, what is a magnetic force, what is the relation between current and magnetism, what is the effect of magnetic charge on the charged wire. We also learned about the right-hand thumb rule and a mathematical equation to find the force on a moving charge wire in a uniform magnetic field.