Question

two insulating infinitely long conductors carrying currents i1 and i2 by mutually perpendicular to each other in the same plane find the magnetic field at the point p (a,b)

Answer 1

Answer:

Explanation:

If there is not given that which charge is greater so you can subtract any two magnetic field in any order but if specific then subtract accordingly tonthat

Answer 2

Answer: The net magnetic field at the point P is $B=$ μ$_{0}$/$2\pi$( $\frac{I_{2} }{b}$ $- \frac{I_{1} }{a}$ )                  

Explanation:

The magnetic field at the point P  due to the current $I_{1}$ can be given by,

                              $B_{1} =$ μ$_{0}$/$4\pi$ × $\frac{2I_{1} }{a}$, directed normally inwards

The magnetic field at the point P due to the current $I_{2}$ can be given by,

                              $B_{2} =$ μ$_{0}$/$4\pi$ × $\frac{2I_{2} }{b}$, directed normally outwards

∴ The net magnetic field at the point P can be given by,

⇒                                 $B= B_{2}-B_{1}$

⇒                                 $B=$ (μ$_{0}$/$4\pi$ × $\frac{2I_{2} }{b}$) $-$ ( μ$_{0}$/$4\pi$ × $\frac{2I_{1} }{a}$)

⇒                                 $B=$ (μ$_{0}$/$2\pi$ × $\frac{I_{2} }{b}$) $-$ (μ$_{0}$/$2\pi$ ×  $\frac{I_{1} }{a}$)

⇒                                 $B=$ μ$_{0}$/$2\pi$( $\frac{I_{2} }{b}$ $- \frac{I_{1} }{a}$ )

∴ The net magnetic field at the point P is $B=$ μ$_{0}$/$2\pi$( $\frac{I_{2} }{b}$ $- \frac{I_{1} }{a}$ )  

               

Concept:The magnetic field is the area around a magnet in which the effect of magnetism is felt.

Magnetic Field created by a Current-Carrying Conductor:

Ampere tells about the magnetic field that a magnetic field is produced whenever an electrical charge is in motion. For our understanding, let us consider a wire through which the current is made to flow by connecting it to a battery. As the current through the conductor increases, the magnetic field increases proportionally. When we move further away from the wire, the magnetic field decreases with the distance. Ampere’s law describes this. According to the law, the equation gives the magnetic field at a distance r from a long current-carrying conductor I.

                                $B=$ μ$_{0}$/$2\pi$ × $\frac{I}{r}$

In the equation, µ0 is a special constant known as the permeability of free space(µ0=4π×10-7 T⋅ m/A).