Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform magnetic field of 0.15 T?
Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.
A straight wire of length l can slide on two parallel plastic rails kept in a horizontal plane with a separation d. The coefficient of friction between the wire and the rails is µ. If the wire carries a current i, what minimum magnetic field should exist in the space in order to slide the wire on the rails?
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.
Two long, straight wires, each carrying a current of 5 A, are placed along the x- and y-axis respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1 m, 1 m), (b) (−1 m, 1 m), (c) (−1 m, −1 m) and (d) (1 m, −1 m).
According to Ampere's circuital law, ______.
Two long parallel wires kept 2 m apart carry 3A current each, in the same direction. The force per unit length on one wire due to the other is ______.
By symmetry, the magnetic field of conductor b exerts a force on conductor a. The relationship between the two forces Fba and Fab is:
A wire carrying a current of 1 A flows East → West in a region where the horizontal component of Earth's magnetic field is B = 3.0 × 10⁻⁵ T directed South → North. The force per unit length on the wire is:
