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College Physics : Faraday's Law of Induction

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Example Question #1 : Electromagnetics

A single string of wire has a resistance of $10\Omega$ $\displaystyle 10\Omega$. If the wire is connected to a 120V $\displaystyle 120V$ power source, what is the strength of the magnetic field 10cm $\displaystyle 10cm$ away from the wire?

$\mu_o=4\pi \times 10^{-7}\frac{T\cdot m}{A}$ $\displaystyle \mu_o=4\pi \times 10^{-7}\frac{T\cdot m}{A}$

Possible Answers:

100T $\displaystyle 100T$

$2.4\times 10^{-5}T$ $\displaystyle 2.4\times 10^{-5}T$

$2.0\times 10^{-6}T$ $\displaystyle 2.0\times 10^{-6}T$

$2.4\times 10^{-7}T$ $\displaystyle 2.4\times 10^{-7}T$

$7.6\times 10^{-5}T$ $\displaystyle 7.6\times 10^{-5}T$

Correct answer:

$2.4\times 10^{-5}T$ $\displaystyle 2.4\times 10^{-5}T$

Explanation:

So this is all about the magnetic field strength around a current carrying wire.

The equation for this is:

$B = \frac{\mu _{0}I}{2\Pi r}$ $\displaystyle B = \frac{\mu _{0}I}{2\Pi r}$

But you must use Ohm's Law (V= IR) $\displaystyle (V= IR)$ in order to find the current in the wire.

Since the wire has $10\Omega$ $\displaystyle 10\Omega$ of resistance and the voltage through the wire is 120V $\displaystyle 120V$, that means the current in the wire is 12A $\displaystyle 12A$.

Being sure to change 10 cm $\displaystyle 10 cm$ into 0.1m $\displaystyle 0.1m$, plug everything in and get the answer, which is

$2.4\times 10^{-5}T$ $\displaystyle 2.4\times 10^{-5}T$

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College Physics : Faraday's Law of Induction

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Example Question #1 : Electromagnetics

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