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We've got two long straight wires carrying current of 5A and placed along x and y axis respectively current flows in direction of positive axes we have to find magnetic field at a) (1 m,1 m) b) (-1 m,1 m) c) (-1 m,-1 m) d) (1 m,-1 m) now using ampere's law $$ \oint_{}^{}B.dl=\mu_oi $$ i found magnetic field for infinite wire be $$ B=\frac{\mu_oi}{2\pi r}$$ where r is distance from the wire but for evaluating the magnetic field we need to know direction of it and thus add it like vector but finding direction of magnetic feild at these point is confusing me , how do i find proper direction of magnetic field ?

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You use the right hand thumb rule to find the direction of the magnetic field due to any current carrying conductor. Here you'll find ways to use the right hand thumb rule:… – udiboy1209 Aug 10 '13 at 14:13
You should also note that $\vec B$ is fundamentally defined as $\mu_0 /4\pi i (\vec {dl}\times\vec r)$, so $(\vec {dl}\times\vec r)$ will give the direction of the magnetic field. – udiboy1209 Aug 10 '13 at 14:17
up vote 3 down vote accepted

The quickest way would be to use the right hand grip rule. From symmetry you may conclude that the magnetic field around each wire forms concentric circular loops around the wire. So now it remains to determine whether clockwise or anticlockwise. To do this, just imagine that you are gripping the wire with your right hand in such a way that your thumb points in the direction of current. Then the remaining fingers point in the direction of the magnetic field. This follows directly from the convention used for doing path integrals - if the closed line integral is performed in the anti-clockwise direction, then the area vector for doing the corresponding surface integral is taken to point towards you. Of course, having thus found the contributions from each individual wire, you would then have to take their vector sum.

On a side note, similar conventions are adopted in mechanics for finding the direction of angular velocity corresponding to clockwise or anticlockwise rotation. Thankfully, the convention is more or less uniform through all areas of physics!

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