If a magnet of 3 Tesla results in EM radiation of about 300 MHz, what radiation will a 9 Tesla magnet produce?
Understand the Problem
The question is asking for the electromagnetic radiation frequency produced by a magnet with a strength of 9 Tesla, given the frequency produced by a 3 Tesla magnet. This involves understanding the relationship between magnetic field strength and the frequency of emitted EM radiation.
Answer
The frequency produced by the 9 Tesla magnet is $3 f_1$.
Answer for screen readers
The frequency produced by the 9 Tesla magnet is $3 f_1$.
Steps to Solve
- Identify the relationship between magnetic field strength and frequency
The frequency of electromagnetic (EM) radiation produced by a magnet is proportional to its magnetic field strength. In this case, we can express this relationship mathematically as:
$$ f_2 = \frac{B_2}{B_1} \cdot f_1 $$
where:
- $f_2$ is the frequency produced by the 9 Tesla magnet,
- $f_1$ is the frequency produced by the 3 Tesla magnet,
- $B_2$ is the strength of the 9 Tesla magnet (9 T),
- $B_1$ is the strength of the 3 Tesla magnet (3 T).
- Substitute values into the equation
Now, substituting the known values into the equation:
$$ f_2 = \frac{9 \text{ T}}{3 \text{ T}} \cdot f_1 $$
- Simplify the equation
Calculating the ratio of the strengths:
$$ f_2 = 3 \cdot f_1 $$
This tells us that the frequency produced by the 9 Tesla magnet is 3 times greater than that produced by the 3 Tesla magnet.
The frequency produced by the 9 Tesla magnet is $3 f_1$.
More Information
This relationship shows that if you increase the magnetic field strength, the frequency of the electromagnetic radiation increases proportionately. This is an application of fundamental physics principles relating to magnets and electromagnetic theory.
Tips
- A common mistake is forgetting that the frequency is directly proportional to the magnetic field strength. Make sure to apply the correct proportionality.
- Miscalculating or misinterpreting the units of Tesla and frequency can lead to errors. Always ensure you are consistent with units.
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