# Homework Help: Induced Magnetic Field

1. Mar 30, 2012

### GeorgeCostanz

1. The problem statement, all variables and given/known data

A parallel-plate capacitor has circular plates with radius 49.0 cm and spacing 2.20 mm. A uniform electric field between the plates is changing at the rate of 1.90 MV/m/s. Find the magnitude of the magnetic field between the plates at a point 12.1 cm from the axis (entirely inside the capacitor).

2. Relevant equations

Ampere's Law for induced current

B(2∏r) = (μ-naught)(ε-naught)(A/d)(dV/dt)

r = .121m
μ-naught = 4∏x10^-7
ε-naught = 8.85x10&-12
d = .0022m
dV/dt = 1.9x10^6 V/(m/s)
A = ∏(.49m)^2

3. The attempt at a solution

the answer is B = 1.28x10^-12 T, but i can't seem to get that answer using my equation. i'd appreciate it if someone could direct me toward my error

thanks

2. Mar 31, 2012

### tiny-tim

Hi George!

(try using the X2 button just above the Reply box )

Show us your full calculations.

(In particular, what did you get for the current through the cylinder of radius 0.121 m ?)

3. Mar 31, 2012

### GeorgeCostanz

@tiny-tim

sure.

Id = [ (E$\circ$A)/d ] * (dV/dt)

Id = [ (E$\circ$*(∏(.492))/.0022 ] * (1.9x106)

Id = .005765 A

i guess

4. Mar 31, 2012

### tiny-tim

mmm … your formula seems to be correct, but i'm not getting the result of 1.28 10-12 T either

5. Mar 31, 2012

### GeorgeCostanz

i got the right answer using the following equation (googled the question)

B = [ (1/2)(r)(dV/dt) ] / C2

C = 3x108 = speed of light in vacuum
dV/dt = 1.9x106
r = .121m

not sure how the 2 equations are related tho

6. Apr 1, 2012

### tiny-tim

ah! i took your word for it instead of looking at the original question …
noooo … that wasn't dV/dt, it was dE/dt !!

is everything clear now?

(and c2 = 1/µoεo, which btw would have have been a lot easier for you to use )

7. Apr 2, 2012

### GeorgeCostanz

wow i'm slow
it's a miracle i've even made it this far

so for r < R,

B = (1/2)µoεo(r)(dE/dt)

thus B = [ (1/2)(r)(dE/dt) ] / C2

guess i got mixed up with all these equations/derivations in front of me

thanks tiny-tim