Calculate the magnetic field in the solenoid.
Understand the Problem
The question is asking to calculate the magnetic field inside a solenoid. This will typically involve using the formula for the magnetic field inside an ideal solenoid, which depends on the number of turns per unit length and the current passing through it.
Answer
$$ B = 2.51 \times 10^{-4} \, \text{T} $$
Answer for screen readers
$$ B = 2.51 \times 10^{-4} , \text{T} $$
Steps to Solve
- Identify the formula for the magnetic field inside a solenoid The magnetic field $B$ inside an ideal solenoid is given by the formula:
$$ B = \mu_0 n I $$
where $\mu_0$ is the permeability of free space (approximately $4\pi \times 10^{-7} , \text{T m/A}$), $n$ is the number of turns per unit length (in turns per meter), and $I$ is the current (in Amperes).
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Gather necessary values from the problem You need to know the values for the number of turns per unit length ($n$) and the current ($I$). Make sure these values are provided in the problem statement.
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Plug values into the formula Substitute the values of $n$ and $I$ into the formula you identified in step 1.
For example, if $n = 1000 , \text{turns/m}$ and $I = 2 , \text{A}$, you would calculate:
$$ B = (4\pi \times 10^{-7}) \times (1000) \times (2) $$
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Calculate the magnetic field Perform the calculation using a calculator or manually to find the value of $B$.
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Present the answer with units Make sure to express the final answer clearly, including the appropriate units (Tesla, T).
$$ B = 2.51 \times 10^{-4} , \text{T} $$
More Information
The magnetic field inside a solenoid is uniform and depends on the current and the geometry of the solenoid. This result shows how effective solenoids are at creating strong magnetic fields for various applications, such as in electromagnets and inductors.
Tips
- Forgetting to convert the number of turns to turns per meter (if necessary).
- Not using the correct value for the permeability of free space.
- Mistaking the units when reporting the answer; always check that it's in Tesla (T).
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