Inductance caused by radio antenna

In summary, a circular loop of wire can be used as a radio antenna and the maximum induced EMF can be calculated using the equation E = A(B_max)(2pi*f), where A is the area of the loop, B_max is the maximum magnetic field strength, and f is the frequency of the radiation.
  • #1
squib
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A circular loop of wire can be used as a radio antenna. If an antenna with a diameter of .215 m is located a distance of 2.50 km away from a from a source with a total power of 57.0 kW at a frequency of 102 MHZ, what is the maximum emf induced in the loop? (Assume that the plane of the antenna loop is perpendicular to the direction of the radiation's magnetic field and that the source radiates uniformly in all directions.)

I figure that B(t) = (Bmax)sin(wt)
Magnetic moment = A*(Bmax)sin(wt)
E=d[A*(Bmax)sin(wt)]/dt = AB_max(cos(wt))w
since I'm looking for max, i set cos(wt) to 1, therefore
E=A(B_max)w = A(B_max)(2pi(frequency))

A=pi(.1075)^2
I=(57*10^3)/((4/3)pi(2.5*10^3)^3))
B_max=sqrt([2I(u_0)]/c)
E=B*A*2*pi*f <--- this does not work however

I am wondering where I went wrong...
 
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  • #2


I can help you solve this problem. Your approach is correct, but there are a few mistakes in your calculations.

Firstly, the equation E = A(B_max)w is incorrect. This equation gives the instantaneous value of the induced EMF, but we are interested in the maximum value.

The correct equation is E = A(B_max)(2pi*f), which you have correctly identified in your next step. However, the value of A you have used is incorrect. The diameter of the antenna is given as 0.215 m, so the radius would be 0.1075 m, and the area should be pi*(0.1075)^2 = 0.0364 m^2.

Next, you have calculated the current incorrectly. The power of the source is given as 57.0 kW, but you have used 57*10^3. The correct value for current would be I = (57*10^3)/((4/3)*pi*(2.5*10^3)^3) = 0.00229 A.

Finally, your calculation for B_max is also incorrect. The correct equation is B_max = sqrt((2*I*u_0)/c), where u_0 is the permeability of free space and has a value of 4*pi*10^-7 N/A^2. Plugging in the correct values, we get B_max = 5.31*10^-6 T.

Now, putting all these values together, we get E = (0.0364)*(5.31*10^-6)*(2*pi*102*10^6) = 3.77 V as the maximum induced EMF in the loop.

I hope this helps clear up your confusion. Let me know if you have any further questions.
 
  • #3


I would like to clarify a few points in this scenario. Firstly, the statement that a circular loop of wire can be used as a radio antenna is not entirely accurate. While a circular loop of wire can indeed be used as an antenna, it is not the only type of antenna and there are many other factors that go into designing an efficient antenna for a specific frequency and power level.

Moving on to the calculation, there are a few issues with the approach taken. Firstly, the formula for calculating the maximum EMF induced in a loop is E = -N * (dΦ/dt), where N is the number of turns in the loop and Φ is the magnetic flux through the loop. In this case, since the loop is perpendicular to the direction of the radiation's magnetic field, the magnetic flux through the loop is simply B_max * A, where A is the area of the loop.

Secondly, the formula for calculating B_max, the maximum magnetic field at the center of the loop, is B_max = μ_0 * I / (2π * r), where μ_0 is the permeability of free space, I is the current in the wire, and r is the radius of the loop. This formula assumes that the current is uniformly distributed along the loop, which may not be the case in this scenario.

Furthermore, the power given in the question is the total power radiated by the source, not the current in the wire. To calculate the current in the wire, we would need to know the impedance of the antenna and the voltage across it.

Finally, it is important to note that the frequency given in the question is 102 MHz, which is in the radio frequency range. At these frequencies, the skin effect becomes significant and the current is not uniformly distributed along the wire. This would affect the calculation of B_max and the resulting EMF induced in the loop.

In conclusion, the approach taken in this calculation is not accurate and does not take into account several important factors. To accurately determine the maximum EMF induced in the loop, a more detailed analysis of the antenna design and the properties of the radiation source would be necessary.
 

1. What is inductance caused by a radio antenna?

Inductance is a property of an electrical circuit that causes a voltage to be induced in the circuit when there is a change in the current. In the case of a radio antenna, the inductance is caused by the changing magnetic field as the radio waves are transmitted or received.

2. How does inductance affect the performance of a radio antenna?

Inductance can affect the performance of a radio antenna in several ways. It can impact the efficiency of the antenna, the frequency range it can transmit or receive, and the overall signal strength.

3. Can inductance be controlled or adjusted in a radio antenna?

Yes, inductance can be controlled and adjusted in a radio antenna by changing the physical design of the antenna. Different shapes and sizes of antennas will have varying levels of inductance, allowing for customization based on the desired performance.

4. Are there any negative effects of inductance in a radio antenna?

Inductance can cause some negative effects on a radio antenna, such as signal distortion and interference. It can also affect the impedance of the antenna, which can impact its ability to match the impedance of the transmission line and result in signal loss.

5. How does the inductance of a radio antenna compare to other components in the circuit?

The inductance of a radio antenna is typically the most dominant inductance in the circuit. This is because the antenna is specifically designed to have a higher inductance to efficiently transmit or receive radio waves. Other components, such as capacitors and resistors, may also have some level of inductance, but it is usually much lower than the antenna's inductance.

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