# Finding Induced EMF in antenna

• kmj9k
In summary, a car with a 75 cm long vertical radio antenna is driving east at 29 m/s. The Earth's magnetic field at this location has a magnitude of 5.9*10^-5 T and points northward, 72° below the horizontal. Using the equation E = BVL, the induced emf between the ends of the antenna is found to be 1.28 mV. However, since the flux must be at right angles to the area, a correction is needed for the 72 degree angle. Using trigonometry, the corrected emf is calculated to be 0.397 mV.
kmj9k
A car with a vertical radio antenna 75 cm long drives due east at 29 m/s. The Earth's magnetic field at this location has a magnitude of 5.9* 10^-5 T and points northward, 72° below the horizontal.
(b) Find the induced emf between the ends of the antenna.

Relevant Equations:
E = BVL

I just tried to plug into E=BVL, using B as (5.9 * 10^-5), V as 29 m/s, and L as 0.75m. I ended up with 1.28 mV, which I know is wrong. But, this problem seems so simplistic, I don't understand what I'm doing wrong.

A simple correction is needed for the 72 degree angle, but it takes a bit of explaining why it is needed:-

Induced Emf is equal to flux linkage change per second from Faraday.

VL gives you a rectangle that is equal to the area of space swept by the Aerial in 1 second.

Through this rectangle magnetic flux is flowing. This flux is cut by the aerial as it sweeps by. Emf = flux cut per second.

Flux = B*Area (this will be the flux cut second so is also the Emf we are after) This is where BVL comes from.

But for this equation to work the flux must be at right angles to the area. If not we need to find the component of the flux density which is at right angles to the area.

This requires a simple bit of trigonometry and this is where the bit about the Earth's field being angled down comes in.

Try drawing this rectangle and putting on the flux vector and seeing what correction is needed for the 72 degrees angle.
(If the angle where 0 degrees all the flux is cut no correction is needed, if it where 90 degrees no flux is cut)

I got it! I used B*Area (or BVL) times the cos of 108 and got 0.397 mV. Thank you so much for your help!

## 1. What is induced EMF in an antenna?

Induced EMF (electromotive force) in an antenna is the electric potential or voltage that is generated in the antenna when it is exposed to an alternating electromagnetic field. This induced EMF is the basis for the transmission and reception of radio waves in antennas.

## 2. How is induced EMF measured in an antenna?

Induced EMF in an antenna can be measured using a voltmeter or oscilloscope. The voltage measured will depend on factors such as the strength of the electromagnetic field, the length and orientation of the antenna, and the frequency of the signal. Higher frequencies will result in higher induced EMF values.

## 3. What factors affect the strength of induced EMF in an antenna?

The strength of induced EMF in an antenna is affected by several factors, including the strength and frequency of the electromagnetic field, the length and orientation of the antenna, and the material and design of the antenna. A longer antenna and a higher frequency field will generally result in a stronger induced EMF.

## 4. How does the shape of an antenna affect induced EMF?

The shape of an antenna can have a significant impact on the induced EMF. Antennas with longer lengths or larger surface areas will generally have a stronger induced EMF, as they are able to intercept more of the electromagnetic field. Additionally, the orientation of the antenna can also affect the induced EMF, with antennas pointing towards the source of the field experiencing a stronger EMF.

## 5. How is induced EMF in an antenna used in practical applications?

Induced EMF in an antenna is used in many practical applications, such as radio and television broadcasting, wireless communication, and radar systems. In these applications, the antenna converts the induced EMF into an electrical signal that can be transmitted or received. The strength of the induced EMF can also be used to determine the distance and direction of the source of the electromagnetic field.

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