Statement 1: If we consider two wires carrying current `l_(1)` and `l_(2)`, then for the Amperian loop show

Then `intB.dl=mu_(0)l_(1)`, even when the second wire is present or not.
Statement-2: At some points magnetic fields of both wires oppose each other and add up at some points and so, in sum over complete path these effects balance each other.

Options

A. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is true, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.

Answer

A

Explanation

Both Statement 1 and 2 are correct and Statement 2 explains the Statement 1

In `B.dlmu_(0)l_("net"),B` the magnetic field exists due to both wires whereas `l_("net")` is current enclosed.
At some points of path encosed `B_("net")=B_(1)+B_(2)` and at some points `B_("net")=B_(1)-B_(2)` and when we some `B.dl`, these effects balance each other and sum does not have effect of `B_(2)`. So `B.dl=mu_(0)l_(1)` with or without the other wire.