Question

Draw a diagram and derive and expression for magnetic field due to an infinitely long straight current carrying conductor at any point.​

Answer 1

Answer:

$\boxed{Your\:Solution}$

Explanation:

→Consider a circular loop of radius r around an infinitely long straight wire carrying current I. As the field lines are circular, the field  vector B  at any point of the circular loop is directed along the tangent to the

[ See the Attachment ]

→circle at that point. By symmetry, the magnitude of field  vector B is same at every point of the circular loop. Therefore,

$\int\limits^a_b {B} \, dl=\int\limits^a_b {B} \, dlcos0=B\int\limits^a_b {} \, dl =B.2\pi r$

$From\:Ampere's\:Circuital\:Law,$

$B.2\pi r=u_{0} I$

∴ B = $\frac{u_{0I} }{2\pi r }$

Answer 2

Answer:

Electric Field: Sheet of Charge

For an infinite sheet of charge, the electric field will be perpendicular to the surface. Therefore only the ends of a cylindrical Gaussian surface will contribute to the electric flux .