Advertisements
Advertisements
Question
Two long straight parallel current-carrying conductors are kept ‘a’ distant apart in the air. The direction of current in both the conductors is the same. Find the magnitude of force per unit length and the direction of the force between them. Hence define one ampere.
Advertisements
Solution
The magnetic induction B1 set up by the current I1 flowing in the first conductor at a point somewhere in the middle of the second conductor is
`B_1 = (mu_0I_1)/(2pia)` ...(1)
The magnetic force acting on the portion P2Q2 of length ℓ2 of the second conductor is
F2 = l2 ℓ2 B1 sin 90° ...(2)
From equation (1) and (2),
F2 = `(mu_0I_1I_2ℓ_2)/(2pia)`, towards first conductor
`F_2/ℓ_2 = (mu_0I_1I_2)/(2pia)` ...(3)
The magnetic induction B2 set up by the current I2 flowing in the second conductor at a point somewhere in the middle of the first conductor is
`B_2 = (mu_0I_2)/(2pia)` ...(4)
The magnetic force acting on the portion P1Q1 of length ℓ1 of the first conductor is
F1 = I1ℓ1B2 sin 90° ...(5)
From equation (3) and (5)
`F_1 = (mu_0I_1I_2ℓ_1)/(2pia)`, towards second conductor
`F_1/ℓ_1 = (mu_0I_1I_2)/(2pia)` ...(6)
The standard definition of 1A
If I1 = I2 = 1A
ℓ1 = ℓ2 = 1m
a = 1m in V/A then `F_1/ℓ_1 = F_2/ℓ_2 = (mu_0 xx 1 xx 1)/(2pi xx 1) = 2 xx 10^-7` N/m
∴ One ampere is that electric current which when flows in each one of the two infinitely long straight parallel conductors placed 1m apart in vacuum causes each one of them to experience a force of 2 × 10-7 N/m.
APPEARS IN
RELATED QUESTIONS
How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.
Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?
A long, straight wire of radius R carries a current distributed uniformly over its cross section. T he magnitude of the magnetic field is
(a) maximum at the axis of the wire
(b) minimum at the axis of the wire
(c) maximum at the surface of the wire
(d) minimum at the surface of the wire.
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.
Consider a 10-cm long piece of a wire which carries a current of 10 A. Find the magnitude of the magnetic field due to the piece at a point which makes an equilateral triangle with the ends of the piece.
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.
Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in figure. Each carries current out of the plane of paper.
- What will be magnetic induction at a point on the axis O? AxisE is at a distance R from each wire.
- What will be the field if current in one of the wires (say A) is switched off?
- What if current in one of the wire (say) A is reversed?
