Calculate the magnetic field at the center of a square loop which carries a current of ` 1.5` A , length of each loop is 50 cm .

Explanation

Current carries through a square loop
` I = 1.5 A`

Length of each loop , ` l = 50 cm = 50 xx 10^(-2)`m .
Magnetic field at the centre of square loop ` B = ? `
Magnetic field due to current carrying straight conductors ( according to boot - savart law )
`B = (mu_(0)I) /(4 pi a) [ Sin phi_(1) + sin phi_(2)] `
` a = 1/2 , phi_(1) = 45^(@) , phi_(2) = 45^(@)`
for a square it has 4 sides . So at the centre of a square , the magnetic field .
`B = 4 xx ( mu_(0)I)/(4 pi l//2) [sin phi_(1) + sin phi_(2)]`
` = (4 xx 4 pi xx 10^(-7) xx 1.5)/( 4pi xx 50 xx 10^(-2)//2 ) [1/sqrt2 + 1/sqrt2]`
` = (4 xx 1.5 xx 2xx 10^(-7))/(sqrt2 xx 25 xx 10^(-2)) `
` = (12 xx 10^(-7))/(1.414 xx 25 xx 10^(-2))`
` = .3395 xx 10^(-5)`
` B = 3.4 xx 10^(-6) T ` .