Question

Two long parallel wires placed side by side on a horizontal table carry the same currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. Determine the direction of the magnetic field at the point exactly midway between the two wires from your point of view. Explain your answer with the aid of labelled diagram. [5 marked​

Answer 1

To find:-

• Magnetic field at the centre between the wires.

Answer:-

We are here given that two long current carrying wires are having same current. We need to find out the magnetic field at the centre between the wires .

We know that for a point between two ends of a wire , magnetic field is given by,

`\implies B =(\mu_0)/(4\pi)(2i)/(d)\\`

where ,

• B is magnetic field.
• i is the current.
• d is the distance .

Now since magnetic field is a vector quantity we need to find out the direction of the field . We can do so by using Right Hand thumb rule .

Right hand thumb rule :-

Hold the wire , in your hand with thumbs towards the direction of the current, then the curling of the fingers would give you the direction of the magnetic field.

For wire AB :-

The direction comes to be down the page .

For wire CD :-

The direction comes to be down the page .

Calculating net magnetic field:-

The net magnetic field will be the sum of both the fields .

`\implies B_(net)=(\mu_0)/(4\pi)(2i)/(d)+(\mu_0)/(4\pi)(2i)/(d) \\`

`\implies B_(net)=(\mu_0)/(4\pi)(4i)/(d)\\`

`\implies \underline{\underline{\green{ B_(net)=(\mu_0i)/( \pi d)}}}\\`

The direction is down the page .

and we are done!