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
Two parallel, long wires carry currents i1 and i2 with i1 > i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 µT. If the direction of i2 is reversed, the field becomes 30 µT. The ratio i1/i2 is
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 copper wire of diameter 1.6 mm carries a current of 20 A. Find the maximum magnitude of the magnetic field `vecB` due to this current.
A long, straight wire carrying a current of 1.0 A is placed horizontally in a uniform magnetic field B = 1.0 × 10−5 T pointing vertically upward figure. Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0 cm from the wire in the same horizontal plane.
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
A long, straight wire carries a current i. Let B1 be the magnetic field at a point P at a distance d from the wire. Consider a section of length l of this wire such that the point P lies on a perpendicular bisector of the section B2 be the magnetic field at this point due to this second only. Find the value of d/l so that B2 differs from B1 by 1%.
Define Ampere in terms of force between two current carrying conductors.
Do magnetic forces obey Newton’s third law. Verify for two current elements dl1 = dlî located at the origin and dl2 = dlĵ located at (0, R, 0). Both carry current I.
When two long, straight, current-carrying conductors are placed parallel to each other and the currents flow in the same direction, the conductors:
According to the definition of the ampere, the constant current maintained in each of two infinitely long, straight, parallel conductors of negligible circular cross-section, placed 1 metre apart in a vacuum, produces a force between them equal to:
