- #1
Reshma
- 749
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From Griffiths again!
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.
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.