Calculate Magnetic Field through Angular Velocity

In summary, the problem involves finding the magnetic field at the pivot of a thin plastic rod with a uniformly distributed charge, rotating at a constant angular speed about the z-axis. The solution involves viewing the situation as a series of concentric current loops and using equations related to angular velocity.
  • #1
Mysterious
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Homework Statement



A thin plastic rod of length L with total charge +q uniformly distributed along only the outer half-length is shown in Fig. 1. The rod is rotated at a constant angular speed w rad/sec about, and perpendicular to, the z-axis. Find the magnetic field B at the pivot, perpendicular to the plane of rotation in terms of L, q and w. (Hint: View the situation as a series of concentric current loops, each with thickness dl.)

RXub3bb.jpg


Homework Equations


No clue which equations will help with angular velocity.


The Attempt at a Solution


I don't know how to go about this problem

Thanks for any help.
 
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  • #2
Do you know a formula that uses velocity?
 

FAQ: Calculate Magnetic Field through Angular Velocity

1. How do you calculate the magnetic field through angular velocity?

To calculate the magnetic field through angular velocity, you need to use the formula B = μ0 * I * ω / (2 * π * r), where B is the magnetic field, μ0 is the permeability of free space, I is the current, ω is the angular velocity, and r is the distance from the center of rotation. This formula is known as the Biot-Savart Law.

2. What is the role of angular velocity in calculating magnetic field?

Angular velocity is the rate of change of angular displacement over time. In the context of calculating magnetic field, it represents the speed at which an object is rotating around a central axis. The higher the angular velocity, the stronger the magnetic field will be.

3. Can you explain the relationship between magnetic field and angular velocity?

The relationship between magnetic field and angular velocity is directly proportional. This means that as the angular velocity increases, the magnetic field also increases. This is because a higher angular velocity results in a stronger magnetic force due to the movement of charged particles.

4. What is the unit of measurement for magnetic field through angular velocity?

The unit of measurement for magnetic field through angular velocity is Tesla (T). This unit is commonly used in the International System of Units (SI) for measuring magnetic fields.

5. How does the distance from the center of rotation affect the magnetic field through angular velocity?

The distance from the center of rotation, represented by the variable r in the formula, has an inverse relationship with the magnetic field. This means that as the distance increases, the magnetic field decreases. This is because the magnetic field strength is inversely proportional to the distance from the source.

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