# Work done by magentic field

• smatik
In summary, the conversation discusses two straight current carrying conductors A and B in a vertical plane with a separation of h and mass per unit length of λ. When raising wire B by a small height δh while keeping wire A fixed, Q-1 asks about the work done by an external agent. Q-2 is then asked if the work done by the magnetic field is zero, to which the answer is no according to the book. The concept of work done by magnetic force is further discussed, with the conclusion that when the force is perpendicular to the motion, the work done is zero.

#### smatik

Two straight current carrying conductors A and B are lying in a vertical plane as shown.The separation between them is h and mass per unit length of wires is λ.Keeping one wire fixed (say A),Bis raised by small hieght δh.
Q-1 What would be the work done by external agent?
Q-2 Will the work done by magnetic field zero?[Answer this question first. I m confused since i was told that the work done by magnetic force(just magnet force not Lorentz) is always zero.But the book says "Work done is non zero",i think the book's wrong]

The book is right work is being done as F.ds is working .
In the case you are talking about F.ds the angle is 90 degree that's why no work done.

is the work done by magnetic force always zero??

See , when magnetic force acts on a charge , it doesn't change its speed , it just gives it centripetal acceleration . And direction of force is always perpendicular to motion .
I can say when ever Force is acting perpendicular to the motion of the body , work done is zero .

I would like to clarify that the work done by the magnetic field is not always zero. The work done by the magnetic force is indeed zero, as the magnetic force is always perpendicular to the displacement of the charged particles and therefore does not do any work. However, in this scenario, the work is being done by an external agent, not just the magnetic force.

To answer the first question, the work done by the external agent would be equal to the change in potential energy of the system. This can be calculated by considering the gravitational potential energy of the raised wire B as well as the change in magnetic potential energy between the two wires. The total work done would be the sum of these two energies.

To answer the second question, the work done by the magnetic field itself (not the external agent) would be zero, as stated earlier. However, the work done by the external agent would not be zero, as there is a change in potential energy in the system. Therefore, the book is correct in stating that the work done is non-zero.

I hope this clarifies any confusion regarding the work done by the magnetic field in this scenario. It is important to differentiate between the work done by the magnetic force and the work done by an external agent in a system involving magnetic fields.

## What is work done by a magnetic field?

Work done by a magnetic field refers to the amount of energy transferred to an object when it moves through a magnetic field. This work is dependent on the strength of the magnetic field, the distance the object travels, and the angle between the direction of motion and the magnetic field.

## How is work done by a magnetic field calculated?

The work done by a magnetic field is calculated by multiplying the magnitude of the magnetic force by the distance the object travels in the direction of the force, and then multiplying by the cosine of the angle between the force and the displacement. The formula for work done by a magnetic field is W = F*d*cos(theta).

## Is work done by a magnetic field always positive?

No, work done by a magnetic field can be positive, negative, or zero. If the angle between the force and displacement is 0 degrees, the work done will be positive. If the angle is 180 degrees, the work done will be negative. If the angle is 90 degrees, the work done will be zero.

## How does work done by a magnetic field affect the motion of an object?

The work done by a magnetic field can either increase or decrease the kinetic energy of an object, depending on the direction of motion and the direction of the magnetic force. If the work done is positive, the object's kinetic energy will increase, causing it to speed up. If the work done is negative, the object's kinetic energy will decrease, causing it to slow down.

## What are some real-life applications of work done by a magnetic field?

Work done by a magnetic field is used in many applications, such as electric motors, generators, and particle accelerators. It is also important in the study of electromagnetism and plays a crucial role in many technological devices, including MRI machines and magnetic levitation trains.