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What is the effect of 2 perpendicular magnetic fields?

My teacher discussed this illustration in class where there were 2 perpendicular magnetic fields. He said that they both cancel each other out. I didn't understand it. I tried to understand it by literally finding out the direction of the magnetic field lines. I'll just attach the illustration here for more clarity. enter image description here

He said that the magnetic field of those two straight wires cancel each other out. I don't understand what that means. Using the right hand thumb rule, the magnetic field due to one of the wires is perpendicular to the magnetic field due to another straight wire.

Can somebody explain why the magnetic fields due to those 2 straight wires cancel each other out?

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    $\begingroup$ Clearly, the magnetic fields from these wires do not cancel each other out. I would guess that you probably misunderstood what your teacher said. Perhaps he meant to say that the two straight wires do not affect the magnetic field at point C, since the currents in these wires flow directly towards/away from C. $\endgroup$
    – Thorondor
    Aug 1, 2021 at 22:40
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    $\begingroup$ Yeah...I misunderstood him. But it's clear now. Besides, I answered my own question :D $\endgroup$
    – HarshDarji
    Aug 1, 2021 at 22:42

4 Answers 4

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Honestly, I have no idea of what is shown in the figure, but I will anyway try to explain it.

The formula for calculating the magnetic field from a electric current is called Biot-Savart law. If you apply this formula to a wire you get a magnetic field of $$B(r) = \frac{\mu_0}{2 \pi} \frac{I}{r}$$ at a point that is distance r away from that wire.

If there is a second (perpendicular) wire with same the current but in opposite direction, the magnetic field will vanish at the half distance between the two wires, because each wire will generate a magnetic field of same strength, but in opposite directions (which you can also see with the right hand thumb rule).

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    $\begingroup$ Ohh wait so you mean the plane of the magnetic fields are perpendicular? And hence they are in opposite directions? $\endgroup$
    – HarshDarji
    Aug 1, 2021 at 22:58
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    $\begingroup$ @HarshDarji no, they are not perpendicular. They are parallel but opposing $\endgroup$ Aug 2, 2021 at 14:20
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If I understand your question correctly, you are asking where the neutral point is located in a bar magnet configuration like this:

perpendicular bar magnets

Correct option is region $I$. Neutral point will be located in region which have opposite magnetic field lines.

net magnetic field

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I drew this image that, while inaccurate, should help you visualize the magnetic fields produced by each section of this circuit.

enter image description here

Either your teacher is wrong or you misunderstood them. Perhaps they meant that those two straight sections have no bearing on the magnetic field at the center point of the two curved regions (point C). That's the most reasonable guess I can make.

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Alright, so I went back to basics. The formula for finding magnetic field (vectorial form) answered my question.

$B = {\mu_o \over 4\pi}{\left( Id\vec l \times \vec r \over r^3 \right)}$

Here, in my question, $Id\vec l$ and $\vec r$ make an angle $0$ with each other making the cross product equal to zero. Hence the magnetic field is zero.

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  • $\begingroup$ That's not the situation $\endgroup$ Aug 2, 2021 at 14:20
  • $\begingroup$ Can you elaborate on how its not the situation? $\endgroup$
    – HarshDarji
    Aug 2, 2021 at 14:34

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