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 through the square loop , I = 1.5 A
Length of each loop, l = 50 cm = `50 xx 10^(-2)` m
According to biot-Savarth law ,
Magnetic field due to a current carrying straight wire
B = `(mu_(0)I)/(4 pi a ) ( sin alpha + Sin beta) = (4 pi xx 10^(-7) xx 1.5)/(4 pi xx ((l)/(2)) ) (sin 45^(@) + sin 45^(@) )`
= `(2 xx 1.5 xx 10^(-7))/(l) ((1)/(sqrt(2)) + (1)/(sqrt(2)) ) = ( 2xx 1.5 xx 10^(-7))/(50 xx 10^(-2)) ((2)/(sqrt(2)) ) `
B = 0.084866 `xx 10^(-5)` T
Magnetic field at a point .P. of centre of current carrying square loop
`B. = 4 "sides" xx B `
= 4 `xx 0.08487 xx 10^(-5) = 0.33948 xx 10^(-5)`
`B. = 3.4 xx 10^(-6) `T