Advertisements
Advertisements
प्रश्न
A hypothetical magnetic field existing in a region is given by `vecB = B_0 vece` where `vece`_r denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x−y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.
उत्तर
Given:
A hypothetical magnetic field existing in a region, `vecB = B_0 vece_r` where denotes the unit vector along the radial direction.
A circular loop of radius a
So, the length of the loop, l = 2πa
Electric current through loop = i
As per the question, the loop is placed with its plane parallel to the X−Y plane and its centre is at (0, 0, d).
Here, angle between the length of the loop and the magnetic field is θ. Magnetic force is given by
`|vecF| = vecilxxvecB`
`vecF = i(2piaxxvecB)`
`vecF = i2piaBsintheta`
=`(i2piaB_0a)/sqrt(a^2 + d^2`
`= (i2piB_0a^2)/sqrt(a^2 + d^2`
APPEARS IN
संबंधित प्रश्न
Two infinitely long straight parallel wires, '1' and '2', carrying steady currents I1 and I2 in the same direction are separated by a distance d. Obtain the expression for the magnetic field `vecB`due to the wire '1' acting on wire '2'. Hence find out, with the help of a suitable diagram, the magnitude and direction of this force per unit length on wire '2' due to wire '1'. How does the nature of this force changes if the currents are in opposite direction? Use this expression to define the S.I. unit of current.
Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current.
How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.
A charged particle goes undeflected in a region containing an electric and a magnetic field. It is possible that
(a) `vecE" || "vecB , vecv" || " vec E `
(b) `vecE "is not parallel" vecB`
(c) `vecv " || " vecB but vecv "is not parallel"`
(d) `vecE" || " vecB but vecv "is not parallel"`
and ```vecE` and `vecB`denote electric and magnetic fields in a frame S and `vecE`→ and `vecB` in another frame S' moving with respect to S at a velocity `vecV` Two of the following equations are wrong. Identify them.
(a) `B_y^, = B_y + (vE_z)/c^2`
(b) `E_y^' = E_y - (vB_z)/(c^2)`
`(c) Ey = By + vE_z`
`(d) E_y = E_y + vB_z`
An electron is moving along the positive x-axis. You want to apply a magnetic field for a short time so that the electron may reverse its direction and move parallel to the negative x-axis. This can be done by applying the magnetic field along
(a) y-axis
(b) z-axis
(c) y-axis only
(d) z-axis only
A long, straight wire carries a current along the z-axis, One can find two points in the x−y plane such that
(a) the magnetic fields are equal
(b) the directions of the magnetic fields are the same
(c) the magnitudes of the magnetic fields are equal
(d) the field at one point is opposite to that at the other point.
A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section. (a) At what points will the resultant magnetic field have maximum magnitude? What will be the maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field?
Figure shows a metallic wire of resistance 0.20 Ω sliding on a horizontal, U-shaped metallic rail. The separation between the parallel arms is 20 cm. An electric current of 2.0 µA passes through the wire when it is slid at a rate of 20 cm s−1. If the horizontal component of the earth's magnetic field is 3.0 × 10−5 T, calculate the dip at the place.
Two parallel wires carry equal currents of 10 A along the same direction and are separated by a distance of 2.0 cm. Find the magnetic field at a point which is 2.0 cm away from each of these wires.
A straight, how wire carries a current of 20 A. Another wire carrying equal current is placed parallel to it. If the force acting on a length of 10 cm of the second wire is 2.0 × 10−5 N, what is the separation between them?
Three coplanar parallel wires, each carrying a current of 10 A along the same direction, are placed with a separation 5.0 cm between the consecutive ones. Find the magnitude of the magnetic force per unit length acting on the wires.
Define Ampere in terms of force between two current carrying conductors.
Three infinitely long parallel straight current-carrying wires A, B and C are kept at equal distance from each other as shown in the figure. The wire C experiences net force F. The net force on wire C, when the current in wire A is reversed will be ______.
