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In Fig. Two long wires W1 and W2, each c...

In Fig. Two long wires `W_1 and W_2`, each carrying current I, are placed parallel to each other and parallel to z-axis. The direction of current in `W_1`is outward and in `W_2` it is inward. Find `vecB` at p and Q.

Text Solution

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Magnetic field at P:
Let `vecB` due to `W_1 be vecB_1` and due to `W_2` be `W_2 and vecB_2`. By symmetry,
`|vecB_1|=|vecB_2|=B`
`implies B_P=2Bcos60^@=B=(mu_0I)/(2pi 2a)=(mu_0I)/(4pia)`
`:. vecB_P=(mu_0I)/(4pia) hatj`

For magnetic field at Q
Magnetic field due to `W_1, B_1=(mu_0I)/(2piasqrt5a)`
Magnetic field due to `W_2, B_2=(mu_0I)/(2pia)`
`vecB_Q=(B_1 cos theta hatj)+(B_2-B_1 sin theta)hati`
`:. vecB_Q=(mu_0I)/(5pia) hatj+((mu_I)/(2pia)-(mu_I)/(10pia))hati`
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