Question

long wire carrying current I is placed along the positive x-axis a unit vector of magnetic field at a point (0,a,a)
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Answer 1

Answer:

Unit vector along the direction of magnetic field is given as

$\hat {dB} = \frac{1}{\sqrt2}(\hat k - \hat j)$

Explanation:

As per Biot Savart Law we know that

$\vec {dB} = \frac{\mu_o i (\vec {dL} \times \hat r)}{4\pi r^2}$

here we need to find the unit vector along the direction of magnetic field

So we have

$\vec {dL} = \hat i$

$\vec r = a\hat j + a\hat k$

now the direction of magnetic field is along

$\vec {dB} = \vec {dL} \times \vec r$

$\vec {dB} = \hat i \times (a \hat j + a\hat k)$

$\vec {dB} = a\hat k - a \hat j$

unit vector along this direction is given as

$\hat {dB} = \frac{1}{\sqrt2}(\hat k - \hat j)$

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Topic : Biot Savart Law

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Answer 2

Explanation:

using biot savart law db. dl*r