Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
Two identical circular coils, P and Q each of radius R, carrying currents 1 A and √3A respectively, are placed concentrically and perpendicular to each other lying in the XY and YZ planes. Find the magnitude and direction of the net magnetic field at the centre of the coils.
At a place, the horizontal component of earth's magnetic field is B and angle of dip is 60°. What is the value of horizontal component of the earth's magnetic field at equator?
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. If the outer coil is rotated through 90° about a diameter, 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 charge of 3.14 × 10−6 C is distributed uniformly over a circular ring of radius 20.0 cm. The ring rotates about its axis with an angular velocity of 60.0 rad s−1. Find the ratio of the electric field to the magnetic field at a point on the axis at a distance of 5.00 cm from the centre.
The magnitude of the magnetic field due to a circular coil of radius R carrying a current I at an axial distance x from the centre is ______.
If we double the radius of a coil keeping the current through it unchanged, then the magnetic field at any point at a large distance from the centre becomes approximately.
A short bar magnet has a magnetic moment of 0. 65 J T-1, then the magnitude and direction of the magnetic field produced by the magnet at a distance 8 cm from the centre of magnet on the axis is ______.
If ar and at represent radial and tangential accelerations, the motion of the particle will be uniformly circular, if:
Two horizontal thin long parallel wires, separated by a distance r carry current I each in the opposite directions. The net magnetic field at a point midway between them will be ______.
