Advertisements
Advertisements
Question
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.
Solution
Given:
Magnitude of current, I = 5 A
Radius of the semi-circular wire, r = 10 cm
∴ Required magnetic field at the centre of curvature
\[B = \frac{1}{2} \times \frac{\mu_0 i}{2r}\]
\[ = {10}^{- 7} \times \frac{5}{10 \times {10}^{- 2}}\]
\[ = 5\pi \times {10}^{- 6} \]
\[ = 1 . 6 \times {10}^{- 5} \] T
APPEARS IN
RELATED QUESTIONS
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.
Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.
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.
A current-carrying, straight wire is kept along the axis of a circular loop carrying a current. This straight wire
Consider the situation shown in figure. The straight wire is fixed but the loop can move under magnetic force. The loop will
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. 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.
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 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?
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.
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 magnetic field at a distance r from a long wire carrying current I is 0.4 tesla. The magnetic field at a distance 2 r is ______.
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(∞)?
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 ______.
