Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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.
Derive the expression for force per unit length between two long straight parallel current carrying conductors. Hence define one ampere.
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?
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
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.
Four long, straight wires, each carrying a current of 5.0 A, are placed in a plane as shown in figure. The points of intersection form a square of side 5.0 cm.
(a) Find the magnetic field at the centre P of the square.
(b) Q1, Q2, Q3, and Q4, are points situated on the diagonals of the square and at a distance from P that is equal to the diagonal of the square. Find the magnetic fields at these points.
A conducting circular loop of radius a is connected to two long, straight wires. The straight wires carry a current i as shown in figure. Find the magnetic field B at the centre of the loop.
If a current I is flowing in a straight wire parallel to x-axis and magnetic field is there in the y-axis then, ______.
A milli voltmeter of 25 milli volt range is to be converted into an ammeter of 25 ampere range. The value (in ohm) of necessary shunt will be ______.
