Kaplan

[greenseeking]

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QUESTION:
A plane polarized electromagnetic wave propagates
with Erms = 30 V/m. What is the power transmitted to
a circular disk of radius r = 2m, if all of the light is
absorbed by the disk and S is perpendicular to the
disk?

A . 10 J/s
B . 30 J/s (KAPLAN'S ANSWER)
C . 60 J/s
D . 90 J/s (MY ANSWER)

Relevant Passage info: Intensity of the wave equals the power transmitted per area.
The intensity, I, can therefore be written as I =Erms^2/(cμ0), where Erms is the root-mean-square electric field.

Kaplan Answer Key: B; P = r^2 × I

My question is: For area, why don't you multiply it pi r^2, since it's a circular disk?
The answer key says that it's r^2 * I but I thought it would be pi r^2 * I.

Thanks for your help.

 

[SpaceBuff12]

QUESTION:
A plane polarized electromagnetic wave propagates
with Erms = 30 V/m. What is the power transmitted to
a circular disk of radius r = 2m, if all of the light is
absorbed by the disk and S is perpendicular to the
disk?

A . 10 J/s
B . 30 J/s (KAPLAN'S ANSWER)
C . 60 J/s
D . 90 J/s (MY ANSWER)

Relevant Passage info: Intensity of the wave equals the power transmitted per area.
The intensity, I, can therefore be written as I =Erms^2/(cμ0), where Erms is the root-mean-square electric field.

Kaplan Answer Key: B; P = r^2 × I

My question is: For area, why don't you multiply it pi r^2, since it's a circular disk?
The answer key says that it's r^2 * I but I thought it would be pi r^2 * I.

Thanks for your help.

Yes, power is equal to the intensity * area; however, you have to know the values of the speed of light, c, and permeability of free space, mu0. The permeability of free-space is 4pi x 10^(-7) H/m and speed of light is 3.0 x 10^8 m/s. Therefore the units work out as such:

P = [4pi m^2 * 900 (V/m)^2 ] / [4pi*10(-7) H/m * 3*10^8 m/s]

= [900 V^2] / [3 * 10^1 H/s]

= 30 V^2*(s/H)

All of those units are SI and I doubt they would make you do a unit conversion in addition to the above problem. Here is the conversion anyway:

V = J*A^-1*s^-1
H = J*A^-2

which gives: 30 J^2 * A^-2 * s^-2 * s * A^2 * J^-1 = 30 J/s

 

[greenseeking]

Hi,
Thank you so much for your explanation! Really cleared things up. I have a follow up question:

I forgot to post the permeability constant. They give us this value mu=4* 10^-7 Ns^2/C^2. So you're saying that it's actually 4 * pi * 10^-7? Does that mean that the problem gave us the wrong value?

 

[greenseeking]

I got the problem wrong because they give us the mu without the pi. So I wasn't able to cross out the pi in the mu constant with the pi in the area. So I got something like 30 * pi and I chose D.

 

[SpaceBuff12]

Hi,
Thank you so much for your explanation! Really cleared things up. I have a follow up question:

I forgot to post the permeability constant. They give us this value mu=4* 10^-7 Ns^2/C^2. So you're saying that it's actually 4 * pi * 10^-7? Does that mean that the problem gave us the wrong value?

Yeah, they gave you an incorrect constant. I doubt there is such a mistake on the MCAT.

 

[greenseeking]

Thanks!