Advertisements
Advertisements
प्रश्न
Answer the following question.
Two infinitely long straight wire A1 and A2 carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A3 carrying current 1.5 I be placed between A1 and A2 so that it experiences no net force due to A1 and A2? Does the net force acting on A3 depend on the current flowing through it?
Advertisements
उत्तर
The force per unit length between two infinitely long, parallel current-carrying wires is given by:
`F = μ_0/(2pi) (I_1I_2)/d`
where:
- I1 and I2 are the currents in the wires,
- d is the separation between them,
- μ0 is the permeability of free space.
Assigning Given Values
- A1 carries current I.
- A2 carries current 2I.
- The distance between A1 and A2 is d.
- A3 carries current 1.5I and is to be placed somewhere between A1 and A2.
For A3 to experience zero net force, the magnitudes of these forces must be equal:
F1 = F2
`μ_0/(2pi) (Ixx1.5I)/x = μ_0/(2pi) (2Ixx1.5I)/((d-x)`
`(1.5I^2)/x = (3I^2)/(d-x)`
`1/x = 2/(d-x)`
d − x = 2x
d = 3x
`x = d/3`
APPEARS IN
संबंधित प्रश्न
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 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.
The magnetic field existing in a region is given by `vecB = B_0(1 + x/1)veck` . A square loop of edge l and carrying a current i, is placed with its edges parallel to the x−y axes. Find the magnitude of the net magnetic force experienced by the loop.
A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2 A is sent through the coil. Find the magnitude of the magnetic field B if the torque acting on the coil is 0.2 N m−1
According to Ampere's circuital law, ______.
The nature of parallel and anti-parallel currents are ______.
Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field produced by one exerts an attractive force on the other. Obtain the expression for this force and hence define 1 ampere.
Beams of electrons and protons move parallel to each other in the same direction. They ______.
