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Two infinitely long wires carry currents...

Two infinitely long wires carry currents 4A and 3A placed along X-axis and Y-axis respectively. Magnetic field at a point p(0,0,d) m will be…..T.

A

`(4 mu_(0))/(2pi d)`

B

`(3 mu_(0))/(2pi d)`

C

`(7 mu_(0))/(2pi d)`

D

`(5 mu_(0))/(2pi d)`

Text Solution

Verified by Experts

The correct Answer is:
D
Magnetic field at point P due to `l_(x)`
`B_(x) =(mu_(0) I_(x))/(2pi d)` (Y- direction)
or `B_(x) =-(mu_(0) cdot 4)/(2pid) hatJ`
Similarly, magnetic field at point P due to `I_(y)`,

`rArr B_(y) =(mu_(0) cdot 3)/(2pi d) a hat i`
`therefore` Resultant magnetic field,
`B = sqrt(B_(x)^(2)+B_(y)^(2))`
`=(mu_(0))/(2 pid) sqrt(4^(2)+3^(2))`
`B =(5 mu_(0))/(2pi d)` (at `-45^(@)` from X-axis)
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