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A large parallel plate capacitor with uniform surface charge [itex]\sigma[/itex] on

upper plate and [itex]-\sigma[/itex] on lower is moving with a constant speed v.

Q1]Find the magnetic field between the plates and also above and below them.

My work:

For a surface charge distribution: [itex]\vec K = \sigma \vec v[/itex]

Magnetic induction: [itex]B = \frac{\mu_0 K}{2}[/itex]

Here both the top plate produces a field:

[tex]B = \frac{\mu_0 K}{2}[/tex]

And the bottom plate produces a field:

[tex]B = -\frac{\mu_0 K}{2}[/tex]

How do I take take into account the directions of these fields in order to calculate the field between them?

Q2] Find the magnetic force per unit area on the upper plate and its direction.

My work:

[tex]\vec F_{mag} = \int \left(\vec K \times \vec B\right)d\vec a[/tex]

So force per unit area is:

[tex]\vec f = \vec K \times \vec B[/tex]

Magnitude of the force would be:

[tex]F = \frac{\mu_0 K^2}{2}[/tex]

How do I determine the direction?

Q3] At what speed 'v' would the magnetic force balance the electrical force?

I need complete assistance on this question.

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# Homework Help: Magnetic field for parallel plate capacitors

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