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Magnetic Fields

Practice Magnetic Fields
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Magnetic Fields

Students will learn the idea of magnetic field lines, how they behave in the situation of permanent magnets and current carrying wires and also how to calculate the magnetic field at an arbitrary distance from the wire. Magnetic fields are usually denoted by the letter B and are measured in Teslas, in honor of the Serbian physicist Nikola Tesla.

Key Equations

B_{\text{wire}} = \frac{\mu_0 I}{2 \pi r}&& \text{Magnetic field at a distance } r \text{ from a current-carrying wire}\\\text{Where }  \mu_0=4 \pi \times 10^{-7} \; \text{Tm/A} && \text{Permeability of Vacuum (approximately same for air also)}







In the example above, a current is running along a wire towards the top of your page. The magnetic field is circling the current carrying wire in loops which are perpendicular to the page. Where these loops intersect this piece of paper, we use the symbol \bigodot to represent where the magnetic field is coming out of the page and the symbol \bigotimes to represent where the magnetic field is going into the page . This convention can be used for all vector quantities: fields, forces, velocities, etc.

Example 1

You are standing right next to a current carrying wire and decide to throw your magnetic field sensor some distance perpendicular to the wire. When you go to retrieve your sensor, it shows the magnetic field where it landed to be 4*10^{-5}\;\text{T} . If you know the wire was carrying 300A, how far did you throw the sensor?



B&=\frac{\mu_oI}{2\pi r}\\r&=\frac{\mu_oI}{2\pi B}\\r&=\frac{4\pi*10^{-7}\:\text{Tm/A}* 300\:\text{A}}{2\pi* 4*10^{-5}\:\text{T}}\\r&=1.5\:\text{m}\\

Watch this Explanation


Magnet and Compass (PhET Simulation)

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Answers to Selected Problems

  1. Both pointing away from north
  2.  3 \times 10^{-6} \text{T}
  3. 5000 A

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