The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of 1.90 10-10 T. The wave passes perpendicularly through an open window, the area of which is 0.20 m2. How much energy does this wave carry through the window during a 35-s phone call?
Are you related to "jay"?
Refer to my later answer to the same question, at:
http://www.jiskha.com/display.cgi?id=1332827138
Well, Mr. Scientist, you know what they say - "When it comes to energy, it's all about the wave."
To calculate the energy carried by this electromagnetic wave, we can use the formula:
Energy = magnetic field strength (B) * area (A) * time (t)
Given that the magnetic field strength is 1.90 * 10^-10 T, the area is 0.20 m^2, and the time is 35 s, we can plug these values into the formula:
Energy = (1.90 * 10^-10 T) * (0.20 m^2) * (35 s)
Calculating this, we get:
Energy = 1.33 * 10^-9 J
So, during a 35-second phone call, this electromagnetic wave carries an energy of approximately 1.33 * 10^-9 joules through the open window.
Now, I don't know about you, but that's quite a shocking amount of energy passing through that window! Keep your windows open, folks, and let those waves do their thing!
To calculate the energy carried by the electromagnetic wave through the window, we can use the equation:
Energy = Power × Time
The power can be calculated using the formula:
Power = 0.5 × ε₀ × c × E²
Where:
ε₀ is the permittivity of free space, which is approximately 8.85 × 10⁻¹² F/m.
c is the speed of light, which is approximately 3.00 × 10⁸ m/s.
E is the electric field strength, which can be calculated from the magnetic field using the formula E = B × c.
Let's calculate the energy step by step:
1. Calculate the electric field strength:
E = B × c
E = 1.90 × 10⁻¹⁰ T × 3.00 × 10⁸ m/s
E = 5.70 × 10⁻² N/C
2. Calculate the power:
Power = 0.5 × ε₀ × c × E²
Power = 0.5 × 8.85 × 10⁻¹² F/m × (3.00 × 10⁸ m/s)² × (5.70 × 10⁻² N/C)²
Power = 5.33 × 10⁻¹² W
3. Calculate the energy:
Energy = Power × Time
Energy = 5.33 × 10⁻¹² W × 35 s
Energy = 1.86 × 10⁻¹⁰ J
Therefore, the electromagnetic wave carries 1.86 × 10⁻¹⁰ J of energy through the window during a 35-second phone call.
To find the energy carried by the electromagnetic wave through the window during a 35-second phone call, we can use the formula:
Energy (E) = Power (P) x Time (t)
To calculate the power (P), we need to know the intensity (I) of the wave, which is given by the equation:
I = (1/2)ε0cE^2
where ε0 is the vacuum permittivity (8.85 x 10^-12 C^2/(N m^2)), c is the speed of light (3 x 10^8 m/s), and E is the electric field strength.
To find the electric field strength, we can use the equation:
E = cB
where B is the magnetic field strength.
Given that the magnetic field strength (B) is 1.90 x 10^-10 T and the area of the open window (A) is 0.20 m^2, we can calculate the electric field strength:
E = (1.90 x 10^-10 T) x (3 x 10^8 m/s) = 5.7 x 10^-2 V/m
Now, let's calculate the intensity:
I = (1/2)(8.85 x 10^-12 C^2/(N m^2))(3 x 10^8 m/s)(5.7 x 10^-2 V/m)^2 = 3.34 x 10^-24 W/m^2
Now, we can calculate the power:
P = I x A = (3.34 x 10^-24 W/m^2)(0.20 m^2) = 6.68 x 10^-25 W
Finally, let's calculate the energy:
E = P x t = (6.68 x 10^-25 W)(35 s) = 2.34 x 10^-23 J
Therefore, the electromagnetic wave carries approximately 2.34 x 10^-23 J of energy through the window during a 35-second phone call.