# What is the amplitude of induced EMF in a magnetic dipole antenna?

• midgic
In summary, a magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius 5.0 cm. The EM wave has frequency 870 kHz, electric field amplitude 0.50 V/m, and magnetic field amplitude 1.7 X 10-9 T. Assuming it is aligned correctly, the amplitude of the induced emf in the coil is -0.50 V/m. The amplitude of the emf induced in an electric dipole antenna of length 5.0 cm aligned with the electric field of the wave is 1.7 X 10-9 T.
midgic
1. A magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius 5.0 cm. The EM wave has frequency 870 kHz, electric field amplitude 0.50 V/m, and magnetic field amplitude 1.7 X 10-9 T.

(b) Assuming it is aligned correctly, what is the amplitude of the induced emf in the coil? (Since the wavelength of this wave is much larger than 5.0 cm, it can be assumed that at any instant the fields are uniform within the coil.)

(c) What is the amplitude of the emf induced in an electric dipole antenna of length 5.0 cm aligned with the electric field of the wave?

## Homework Equations

(b) $$emf = -N\frac{\Delta \Phi}{\Delta t}$$

$$\Phi = B \times A$$

(c) ?

## The Attempt at a Solution

(b) The frequency is 870 kHz, so one oscillation takes a time of $$1.15\times 10^{-6}~s$$

$$\frac{\Delta \Phi}{\Delta t}= \frac{\Delta B}{\Delta t}~\times A = \frac{(2)(1.7\times 10^{-9}~T)}{(\frac{1}{2})(1.15\times 10^{-6}~s)}~\times \pi~(0.050~m)^2$$

Would this be the way to find $$\frac{\Delta \Phi}{\Delta t}$$

(c) I'm not sure where to start.

Thanks for your help.

Last edited by a moderator:
Delta2
For ## \frac{\Delta{\Phi}}{\Delta t}##, ## B=B_o \cos(\omega t) ##, so that ## \frac{dB}{dt}=-\omega \sin(\omega t) =\omega \cos(\omega t+\pi/2) ##, where ## \omega=2 \pi f ##. The factor ## \omega ## is the correct factor to use here. Using ## f=\frac{1}{T} ## will be missing the ## 2 \pi ## factor. ## \\ ## And (c) is simple. You just need to convert ## L=5.0## cm to meters. They give you the electric field ## E ## for the electromagnetic wave. The EMF for that case is ## \mathcal{E}=\int E \cdot dl=E L ##.

Delta2 and midgic
Thank you so much for your reply. That makes sense for part (b).

I think I can write it like this: (?)
$$B = B_0~cos(\omega~t)$$
$$\frac{dB}{dt} = -B_0~\omega~sin(\omega~t)$$
Then $$emf = -N~B_0~(2\pi~f) \times \pi~r^2$$

And for part (c)...well as you point out, that's quite straight-forward. I should have been able to do that one.

Thanks very much for your help.

Delta2 and Charles Link
They just want the amplitude for part (b) so don't include the minus sign in the answer for the amplitude of the EMF. The minus sign is just the result of a phase shift.

## What is induced EMF in an antenna?

Induced EMF, or electromagnetic force, is a phenomenon that occurs when a changing magnetic field induces an electric current in a conductor, such as an antenna. This current is responsible for the transmission and reception of electromagnetic waves, allowing an antenna to send and receive signals.

## How is induced EMF generated in an antenna?

Induced EMF is generated in an antenna through the principle of electromagnetic induction. When a varying magnetic field passes through a conductor, it creates a fluctuating electric field, which in turn generates an electric current. In the case of an antenna, the varying magnetic field is created by the radio waves being transmitted or received.

## 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 frequency and amplitude of the electromagnetic waves, the length and orientation of the antenna, and the materials used in the antenna's construction. Additionally, the presence of interference or obstacles can also impact the strength of induced EMF in an antenna.

## How does the length of an antenna affect induced EMF?

The length of an antenna is directly related to the strength of induced EMF. As a general rule, the longer the antenna, the stronger the EMF will be. This is because a longer antenna allows for a larger surface area for the electric field to interact with, resulting in a stronger induced current.

## Can induced EMF be harmful to humans?

Induced EMF in an antenna is typically at a low level and is not harmful to humans. However, if someone is in close proximity to a high-powered antenna, such as a cell phone tower, they may experience some minor effects, such as heat or tingling sensations. It is important to follow safety guidelines and regulations when working with or around high-powered antennas to avoid potential health risks.

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