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In class today we were given the situation of a single DC current carrying wire was trying to deflect a compass needle. We were told that the magnetic field of the earth was $5\times10^{-5}T$ and we had to rite down a formula describing how far we must be from this wire in order to be sure it wouldsignificantly deflect a compass needle from magnetic north.

Does this have anything to do with the formula

$f = \frac{\mu_oI_1I_2}{2\pi d}$ or am i parking up the wrong tree, any help where to start would be great.

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    $\begingroup$ What do you think that the equation that you wrote down means? $\endgroup$
    – user93237
    Commented May 6, 2018 at 4:28
  • $\begingroup$ It means the force per unit length of the wire but that’s the only formula I know to do with a wire so could we say that the compass needle is another wire $\endgroup$
    – Tom Heeley
    Commented May 6, 2018 at 4:31
  • $\begingroup$ The formula you have quoted is the force per unit length between two wires carrying currents $I_1$ and $I_2$. What you want is the equation for the magnetic field generated by a single wire. That nice Mr. Google can help :-) $\endgroup$
    – John Rennie
    Commented May 6, 2018 at 4:45
  • $\begingroup$ You can find the answer here: bfy.tw/HzxY $\endgroup$
    – my2cts
    Commented May 6, 2018 at 11:15
  • $\begingroup$ @my2cts not that helpful $\endgroup$
    – Tom Heeley
    Commented May 6, 2018 at 19:21

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You will have to understand the physical concept when ever you get such questions.

Few points to be considered.

  1. The current carrying wire creates a magnetic field and when we get away from it the intensity reduced. The more you are close to it, the intensity increases.

  2. When you take the compass near to the wire it starts getting deflected. The more closer your are more the deflection.

So what you have to find is a place where the magnetic field intensity of the wire is equal to the earths magnetic field. Make sure the directions are opposite since the field is a vector.

Following is the equation to find the Magnetic field intensity created by a current carrying wire and this should be made equal to the intensity of the earths field value and solve it for r.

enter image description here

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