Question

A long, straight wire carrying a current I₁ is placed on a horizontal table in front of you and the direction of the current points +x axis. The magnetic field produced by the current I₁ at a point 5 cm above the wire is 0.2 T. A second parallel wire carrying a current I₂ = 3I₁ is placed 10 cm above the first wire and the direction of the current also points +x axis. What is the magnitude of the net magnetic field produced by these two currents at a point 5 cm above the table?

Answer 1

The magnetic field () due to 'long' current ( ) carrying straight wire at a prpandicular distance from it is given as

___________________________ relation 1

magnitude of magnetic field is given as

__________________________ relation 2

Here we can see that the magnetic field is directly proportion to magnitude of current through the wire

_____________________________relation 2

Let,

= Magnetic field at 5 cm above table due to bottom wire = 0.2 T

= Magnetic field at 5 cm above table due to top wire

= Current through bottom wire =

= current through top wire =

= 5 cm for both wires ( distance between wires and point 5 cm above table)

Using proprtionality relation 2 we get

(everything else cancels out since it is constant for both wires )

Using above values in this relation we get

this gives

Since the currents are flowing in same direction in bothe wires but distance vectors for both wires are directed apposite to each other , the magnetic field vectors and are directed opposite to each other.

so magnitude of net magnetic field is given as