Advertisements
Advertisements
प्रश्न
The given figure shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. Calculate the magnetic field in the region r < a and r > a.
Advertisements
उत्तर
- Consider the case r > a. The Amperian loop, labelled 2, is a circle concentric with a cross-section. For this loop, L = 2πr
Using Ampere circuital Law, we can write,
B(2πr) = μ0I, `B = (mu_0I)/(2pir), B ∝ 1/r` (r > a) - Consider the case r < a. The Amperian loop is a circle labelled 1. For this loop, taking the radius of the circle to be r, L = 2πr
Now the current enclosed Ie is not I but is less than this value. Since the current distribution is uniform, the current enclosed is,
`I_e = I((pir^2)/(pia^2)) = (Ir^2)/a^2` Using Ampere’s law, B(2πr) = `mu_0 (Ir^2)/a^2`
B = `((mu_0I)/(2pia^2))r`
B ∝ r (r < a)
APPEARS IN
संबंधित प्रश्न
Write Maxwell's generalization of Ampere's circuital law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is `I=varepsilon_0 (dphi_E)/dt,`where ΦE is the electric flux produced during charging of the capacitor plates.
A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be 0.27 T. What is the magnetic force on the wire?
A hollow tube is carrying an electric current along its length distributed uniformly over its surface. The magnetic field
(a) increases linearly from the axis to the surface
(b) is constant inside the tube
(c) is zero at the axis
(d) is zero just outside the tube.
In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero
(a) outside the cable
(b) inside the inner conductor
(c) inside the outer conductor
(d) in between the tow conductors.
Consider the situation described in the previous problem. Suppose the current i enters the loop at the points A and leaves it at the point B. Find the magnetic field at the centre of the loop.
A thin but long, hollow, cylindrical tube of radius r carries i along its length. Find the magnitude of the magnetic field at a distance r/2 from the surface (a) inside the tube (b) outside the tube.
A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.
Define ampere.
Calculate the magnetic field inside and outside of the long solenoid using Ampere’s circuital law
A solenoid of length 0.6 m has a radius of 2 cm and is made up of 600 turns If it carries a current of 4 A, then the magnitude of the magnetic field inside the solenoid is:
