Two identical circular coils are separated by a distance twice the radius of either of the coil. If n = 2, r = 0.08 m, i = 3A, then calculate the resultant magnetic field at the mid point of the line joining their centres, for currents in the same sense and opposite sense in the two circular coils.

Explanation

Give : n =2, r = -0.08 m, i = 3A
Magnetic field at a point on the axis,
`" "=(mu_(0)/(4pi))((2pinir^(2))/((r^(2)+x^(2))^(3//2)))`
At P, `" "B=(10^(-7) times 2 times 3.142 times 2 times 3 times r^(2))/(r^(2)+r^(2))^(3//2)`
`" "=(37.7 times 10^(-7) times r^(2))/(2.828 times r^(3))`
`" "=(13.33 times 10^(-7))/(0.08)`
`" "=1.67 times 10^(-5)T`
For currents in the same direction `B_(p)=2B=3.34 times 10^(-5)T`
For currents in the same opposite direction `B_(p)^(')=` zero.