Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Magnitude of current, I = 6 A
Radius of the semi-circular wire, r = 10 cm
Angle subtended at the centre, θ = 120° = \[\frac{2\pi}{3}\]
∴ Required magnetic field at the centre of curvature
\[B = \frac{\mu_0 i}{2r}\frac{\theta}{2\pi}\]
\[ = \frac{4 \times {10}^{- 7} \times 5}{2 \times 10 \times {10}^{- 2}} \times \frac{2\pi}{3 \times 2\pi}\]
\[ = 4\pi \times {10}^{- 6} \]
\[ = 1 . 26 \times {10}^{- 5} T\]
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.
Use Biot-Savart's law to find the expression for the magnetic field due to a circular loop of radius 'r' carrying current 'I', at its centre ?
Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force. The loop will
A steady electric current is flowing through a cylindrical conductor.
(a) The electric field at the axis of the conductor is zero.
(b) The magnetic field at the axis of the conductor is zero.
(c) The electric field in the vicinity of the conductor is zero.
(d) The magnetic field in the vicinity of the conductor is zero.
Figure shows a square loop ABCD with edge-length a. The resistance of the wire ABC is r and that of ADC is 2r. Find the magnetic field B at the centre of the loop assuming uniform wires.
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 circular loop of radius 20 cm carries a current of 10 A. An electron crosses the plane of the loop with a speed of 2.0 × 106 m s−1. The direction of motion makes an angle of 30° with the axis of the circle and passes through its centre. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane.
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 circular loop of radius r carrying a current i is held at the centre of another circular loop of radius R(>>r) carrying a current I. The plane of the smaller loop makes an angle of 30° with that of the larger loop. If the smaller loop is held fixed in this position by applying a single force at a point on its periphery, what would be the minimum magnitude of this force?
Find the magnetic field B due to a semicircular wire of radius 10.0 cm carrying a current of 5.0 A at its centre of curvature.
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?
A circular loop of radius 4.0 cm is placed in a horizontal plane and carries an electric current of 5.0 A in the clockwise direction as seen from above. Find the magnetic field (a) at a point 3.0 cm above the centre of the loop (b) at a point 3.0 cm below the centre of the loop.
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 ______.
A small square loop of wire of side l is placed inside a large square loop of side L (L >> l). The loop is coplanar and their centers coincide. The mutual inductance of the system is proportional to is
If ar and at represent radial and tangential accelerations, the motion of the particle will be uniformly circular, if:
Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line intergral
`ℑ(L ) = |int_(-L)^L B.dl|` taken along z-axis.
- Show that ℑ(L) monotonically increases with L.
- Use an appropriate Amperian loop to show that ℑ(∞) = µ0I, where I is the current in the wire.
- Verify directly the above result.
- Suppose we replace the circular coil by a square coil of sides R carrying the same current I. What can you say about ℑ(L) and ℑ(∞)?
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).
