Question

The ratio of magnetic field at the centre of circular loop to magnetic field at the centre of square loop which are made by a constant length current carrying wire

Answer 1

Answer:

The answer will be  π^2/8√2

Explanation:

Let the length of a circular loop is l

Therefore l = 2 π r

Now let the magnetic field for the circular loop = b = μo/4π x  2 π i/r

                            where i is the current passing through it

           b =  μo/4π x  4π^2 i/r

Now the length of one side of a square loop is l

Therefore l = 4a

Now again let the magnetic field for the square loop = b =4 xμo/4π x2 √2i/a

                              b = μo/4π x 8√2i/(1/2)π r

Hence the ratio for between the magnetic field for circular and square is

μo/4π x  4π^2 i/r/μo/4π x 8√2i/(1/2)π r = π^2/8√2