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Equal currents are flowing in three infi...

Equal currents are flowing in three infinitely long wires along positive `x,y` and `z` -directions. The magnetic field at a point `(0,0-a)` would be (`i=`current in each wire)

Text Solution

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`bar(B)` due to in x - direction `vec(B)_(x) = (mu_0i)/(2 pia) hatj`
`barB` due to current in y - direction
`barB_y = (mu_0i)/(2pia)(- hati)`
`barB` due to current in Z-direction is zero since the point is present on the line of the current carrying conductor.
`B_Z = 0`
`bar (B) = bar(B_x) + bar(B_y) + bar(B_z)`
`bar(B)_("(0,0,a)")= (mu_0i)/(2pia) hatj - (mu_0i)/(2pia)hati`
`|barB_("(0,0,-a)")|=(mu_0i)/(2pia) sqrt(2)`
`|barB| = (mu_0i)/(2pia)sqrt(2)`
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