when equal current is passed through two coils , equal magnetic field is produced at their centres If the - Physics - Moving Charges And Magnetism

Question

when equal current is passed through two coils , equal magnetic
field is produced at their centres If the ratio of number of turns
in the coils is 8:15 , then what would be the ratio of their radii
?

Ved Prakash Lakhera · Accepted Answer

The magnetic field at the centre of a coil of radius r is given by,B = μ0 I2 r
 In the given cases coil one of radius r1 and coil two of radius r2and their corresponding number of turns 8n and 15n are also given
Therefore B1 = μ0 I×8n2 r1   and   B2 = μ0 I×15n2 r2But B1 = B2, therefore  μ0 I×8n2 r1 =μ0 I×15n2 r2  or    r1/ r2 = 8/15

when equal current is passed through two coils , equal magnetic field is produced at their centres. If the ratio of number of turns in the coils is 8:15 , then what would be the ratio of their radii ?