# Velocity of a moving conducting bar in a magnetic field

• Linus Pauling
In summary, a conducting bar of length l and mass m, resting on frictionless rails of length d, will experience a force to the right when a current flows through it in an upward pointing uniform magnetic field of strength B. The direction of the current is determined by the right hand rule. The speed of the bar as it leaves the rails at the right end can be expressed as vf = (BId)/m, where I is the current and d is the displacement distance. The acceleration of the bar can be found using kinematic equations with the initial velocity being zero.

#### Linus Pauling

1. A conducting bar of length l and mass m rests at the left end of the two frictionless rails of length d in the figure. A uniform magnetic field of strength B points upward. In which direction, into or out of the page, will a current through the conducting bar cause the bar to experience a force to the right? Find an expression for the bar's speed as it leaves the rails at the right end. Express your answer in terms of the variables l, I, B, m, and d.

2. F = Il x B

3. By the right hand rule, the current must be flowing "into the page." However, it isn't clear to me how to get the velocity expression. My instinct would be that v is directly proportional to I, B, and d and inversely proportional to l and m.

By using the relevant equation you have found the force F. Mass of the bar is given. Find the acceleration.
Initial velocity of the bar is zero. You want to find the final velocity when the bar leaves the rails by displacing through a distance d.
Using kinematic equation find vf.

## 1. What is the definition of velocity in the context of a moving conducting bar in a magnetic field?

Velocity refers to the speed and direction at which the conducting bar is moving in the presence of a magnetic field.

## 2. How is the velocity of a conducting bar in a magnetic field determined?

The velocity of a conducting bar in a magnetic field is determined by the strength of the magnetic field, the length of the bar, and the angle between the bar and the magnetic field.

## 3. What is the effect of increasing the magnetic field strength on the velocity of a conducting bar?

Increasing the magnetic field strength will also increase the velocity of the conducting bar, as long as the other factors remain constant.

## 4. How does the length of the conducting bar affect its velocity in a magnetic field?

The longer the conducting bar, the larger the distance it has to travel in the same amount of time, resulting in a higher velocity.

## 5. Can the velocity of a conducting bar in a magnetic field be changed by altering the angle between the bar and the magnetic field?

Yes, the velocity of a conducting bar can be changed by altering the angle between the bar and the magnetic field. A larger angle will result in a lower velocity, while a smaller angle will result in a higher velocity.