Electric field from a rotating coaxial ring

The factor of 1/2 comes from the fact that the wire is rotating and only half of the wire contributes to the magnetic field at any given point on the axis, since the other half is moving away from the point. Therefore, the total magnetic field is half of what it would be for a stationary ring with the same current. In summary, the magnetic field on the axis at a distance z from a wire bent into a rotating ring of radius a and with angular velocity ω is equal to half of the magnetic field for a stationary ring with the same current, given by B = \frac{\mu_0 I a^2}{2(a^2 + z^2)^{3/2}}\hat{z}.
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Homework Statement



A wire with uniform charge density λ per unit length is bent into a ring of radius a and rotates with angular velocity ω about an axis through its centre and perpendicular to the plane of the ring. Find the magnetic field on the axis at a distance z from the ring.


Homework Equations



The magnetic field at a distance z from a ring with current I flowing through it is

[tex]B = \frac{\mu_0 I a^2}{2(a^2 + z^2)^{3/2}}\hat{z}[/tex]


The Attempt at a Solution



I assumed that the magnetic field would be the same as in a stationary ring with current I, where in this case I would be given by λωa. However, the solution appears to be less than this by a factor of 1/2 and I am completely at a loss as to where this extra 1/2 comes from.
 
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  • #2
Anyone?
 
  • #3
Ack, I just realized that the title should be magnetic field, not electric field.
 
  • #4
I think you are right.
 
  • #5




Your assumption is correct, the magnetic field on the axis at a distance z from a rotating ring with charge density λ and angular velocity ω is given by B = \frac{\mu_0 I a^2}{2(a^2 + z^2)^{3/2}}\hat{z}. However, the factor of 1/2 in the solution comes from the fact that the electric field from the rotating ring is not constant, but rather varies with time. This causes a decrease in the magnetic field strength compared to a stationary ring with the same current. This phenomenon is known as the Ampere's law correction factor and is represented by the 1/2 in the equation.
 

1. What is an electric field from a rotating coaxial ring?

An electric field from a rotating coaxial ring refers to the distribution of electric charge around a ring that is rotating about its axis. The electric field is created by the movement of electrons and can be measured at different points surrounding the ring.

2. How is the electric field from a rotating coaxial ring calculated?

The electric field from a rotating coaxial ring can be calculated using the equation E = (k*q*r)/r^2, where E is the electric field, k is the Coulomb's constant, q is the charge on the ring, and r is the distance from the center of the ring.

3. What factors affect the strength of the electric field from a rotating coaxial ring?

The strength of the electric field from a rotating coaxial ring is affected by the magnitude of the charge on the ring, the distance from the ring, and the speed of rotation. The direction of the electric field is also affected by the direction of rotation.

4. What is the direction of the electric field from a rotating coaxial ring?

The direction of the electric field from a rotating coaxial ring is tangential to the ring at any given point. This means that the electric field points in a direction parallel to the ring's circumference at that point.

5. How is the electric field from a rotating coaxial ring different from a stationary ring?

The electric field from a rotating coaxial ring is different from a stationary ring in that it has a changing magnitude and direction due to the motion of the ring. A stationary ring has a constant electric field that does not change with time.

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