If a 4 Tesla magnet produces EM radiation of about 300 MHz, what frequency will an 8 Tesla magnet produce with its field directed opposite?

Understand the Problem

The question is asking for the frequency of electromagnetic radiation produced by an 8 Tesla magnet, given that a 4 Tesla magnet produces radiation at 300 MHz. It implies a direct relationship between the magnetic field strength and the frequency of the emitted radiation.

Answer

$600 \, \text{MHz}$

Steps to Solve

Identify the relationship between magnetic field and frequency

We know that the frequency $f$ of the electromagnetic radiation is directly proportional to the magnetic field strength $B$. This relationship can be expressed as:

$$ f_2 = f_1 \cdot \frac{B_2}{B_1} $$

where:

$f_1 = 300$ MHz (frequency from 4 Tesla)
$B_1 = 4$ Tesla (initial magnetic field)
$B_2 = 8$ Tesla (new magnetic field)
$f_2$ is the frequency at 8 Tesla.

Substitute the values into the equation

Next, we substitute the known values into the equation:

$$ f_2 = 300 , \text{MHz} \cdot \frac{8 , \text{Tesla}}{4 , \text{Tesla}} $$

Calculate the new frequency

Now we calculate $f_2$:

$$ f_2 = 300 , \text{MHz} \cdot 2 = 600 , \text{MHz} $$

This means that the frequency of electromagnetic radiation produced by the 8 Tesla magnet is 600 MHz.

The frequency of electromagnetic radiation produced by an 8 Tesla magnet is $600 , \text{MHz}$.

More Information

This problem relates to the principles of electromagnetism, specifically the relationship between the magnetic field and the frequency of electromagnetic radiation. Higher magnetic fields lead to higher frequencies which can be important in various applications, including particle physics and medical imaging techniques like MRI.

Tips

Confusing the relationship between frequency and magnetic field. Remember that an increase in magnetic field results in a proportional increase in frequency.
Failing to maintain proper units during calculations. Ensure that MHz (megahertz) is consistently used as a unit of frequency.

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