Advertisements
Advertisements
Question
Use Biot-Savart law to derive the expression for the magnetic field on the axis of a current carrying circular loop of radius R.
Draw the magnetic field lines due to a circular wire carrying current I.
Advertisements
Solution
I = Current in the loop
R = Radius of the loop
X-axis = Axis of the loop
X = Distance between O and P
dl = Conducting element of the loop
According to the Biot–Savart law, the magnetic field at P is
`dB=(mu_0)/(4pi) (I|dlxxr|)/r^3`
r2 = x2 + R2
|dl × r| = rdl (Because they are perpendicular)
`:.dB=mu_0/(4pi) (Idl)/((x^2+R^2))`
dB has two components: dBx and dB⊥. dB⊥ is cancelled out and only the x-component remains.
∴ dBx= dBcos θ
`costheta= R/(x^2+R^2)^(1/2)`
`:.dB_x=(mu_0Idl)/(4pi) R/(x^2+R^2)^(3/2)`
Summation of dl over the loop is given by 2πR.
`:.B=B=B_xhati=(mu_0IR^2)/(2(x^2+R^2)^(3/2))hati`
APPEARS IN
RELATED QUESTIONS
Using Biot-Savart law, deduce the expression for the magnetic field at a point (x) on the axis of a circular current carrying loop of radius R. How is the direction of the magnetic field determined at this point?
A current-carrying, straight wire is kept along the axis of a circular loop carrying a current. This straight wire
Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.
A circular loop of radius R carries a current I. Another circular loop of radius r(<<R) carries a current i and is placed at the centre of the larger loop. The planes of the two circles are at right angle to each other. Find the torque acting on the smaller loop.
A piece of wire carrying a current of 6.00 A is bent in the form of a circular are of radius 10.0 cm, and it subtends an angle of 120° at the centre. Find the magnetic field B due to this piece of wire at the centre.
A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?
If ar and at represent radial and tangential accelerations, the motion of the particle will be uniformly circular, if:
An electron is projected along the axis of a circular conductor carrying some current. Electron ______
The fractional change in the magnetic field intensity at a distance 'r' from centre on the axis of the current-carrying coil of radius 'a' to the magnetic field intensity at the centre of the same coil is ______.
(Take r < a).
