Two parallel coaxial circular coils of equal radius R and equal number of turns N carry equal currents I in the same direction and are separated by a distance `2R`. Find the magnitude and direction of the net magnetic field produced at the mid-point of the line joining their centres.

Two parallel coaxial circular coils of equal radius R and equal number of turns N, carry N carry equal currents I in the same direction and are separated by a distance 2R. Find the magnitude and direction of the magnetic field produced at the mid point of the joining their centres.

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, B= (mu_0IR^2N)/(2(x^2+R^2)^(3/2)) . Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by, B=0.72 (mu_0NI)/R approximately.

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by B=(mu_0IR^2N)/(2(x^2+R^2)^(3//2)) (a) Show that this reduces to the familiar result for field at the centre of the coil. (b) Consider two parallel coaxial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R and is given by B=0*72(mu_0NI)/(R) approximately. [Such as arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its center is given by B=(mu_0IR^2N)/(2(x^2+R^2)^(3//2)) (a) Show that this reduces to the familiar result for field at the centre of the coil. (b) Consider two parallel coaxial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R and is given by B=0*72(mu_0NI)/(R) approximately. [Such as arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.]