Question

an infinite wire carrying current is kept along z axis carrying current along the positive z axis . magnetic field at a point (a,a,0) is​

Answer 1

Answer:

an infinite wire carrying current is kept along z axis carrying current

Answer 2

Given:

An infinite wire carrying current is kept along z axis carrying current along the positive z axis .

To find:

Magnetic field at a point (a,a,0)

Calculation:

Net distance of point from wire

$d = \sqrt{ {a}^{2} + {a}^{2} }$

$= > d = \sqrt{2 {a}^{2} }$

$= > d = a \sqrt{2}$

Now , magnetic field intensity be B ;

$B = \dfrac{ \mu_{0}}{4\pi} \bigg \{ \dfrac{2i}{d} \bigg \}$

$= > B = \dfrac{ \mu_{0}}{4\pi} \bigg \{ \dfrac{2i}{a \sqrt{2} } \bigg \}$

$= > B = \dfrac{ \mu_{0}}{4\pi} \bigg \{ \dfrac{ \sqrt{2} i}{a } \bigg \}$

$= > B = \dfrac{ \mu_{0}}{2 \sqrt{2} \pi} \bigg \{ \dfrac{ i}{a } \bigg \}$

So, final answer is:

$\boxed{ \bf{B = \dfrac{ \mu_{0}}{2 \sqrt{2} \pi} \bigg \{ \dfrac{ i}{a } \bigg \}}}$