Advertisements
Advertisements
Question
A wire AB is carrying a steady current of 10 A and is lying on the table. Another wire CD carrying 6 A is held directly above AB at a height of 2 mm. Find the mass per unit length of the wire CD so that it remains suspended at its position when left free. Give the direction of the current flowing in CD with respect to that in AB. [Take the value of g = 10 ms−2]
Advertisements
Solution
Force per unit length between the current carrying wires is given as:
`F = (μ_0)/(4pi) (2I_1I_2)/r `,where I1 = current in wire AB = 10 A and I2 = current in wire CD = 6 A`
r = distance between wires = 2 mm = 2 × 10-3 m.
Let m be the mass per unit length of wire CD. As the force balances the weight of the wire
`therefore (μ_0)/(4pi) (2I_1I_2)/r = mg => 10^-7 xx (2xx10xx6)/(2xx10^-3) = m xx 10`
`therefore m = 10^-7 xx (2 xx 10 xx xx 6)/(2 xx 10^-3) xx 1/10 = 6 xx 10^-4 kg \ m^-1`
APPEARS IN
RELATED QUESTIONS
Derive the expression for the magnetic field due to a solenoid of length ‘2l’, radius ‘a’ having ’n’ number of turns per unit length and carrying a steady current ‘I’ at a point
on the axial line, distance ‘r’ from the centre of the solenoid. How does this expression compare with the axial magnetic field due to a bar magnet of magnetic moment ‘m’?
The magnetic field inside a tightly wound, long solenoid is B = µ0 ni. It suggests that the field does not depend on the total length of the solenoid, and hence if we add more loops at the ends of a solenoid the field should not increase. Explain qualitatively why the extra-added loops do not have a considerable effect on the field inside the solenoid.
A tightly-wound, long solenoid carries a current of 2.00 A. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of 1.00 × 108 rev s−1. Find the number of turns per metre in the solenoid.
A solenoid is defined as a long helical coil of insulated wire with many closely spaced turns. Which geometric condition must it satisfy to be classified as a 'long' solenoid?
During the construction of a solenoid, why is enamelled copper wire used for winding the helical turns?
In the working principle of a solenoid, how does each individual turn of the coil behave?
Why is the magnetic field approximately zero outside a long solenoid?
In the Ampere's Law derivation for a solenoid, what is the contribution of the perpendicular sides \(bc\) (inside to outside) and \(da\) (outside to inside) to \(\oint \vec{B} \cdot d\vec{l}\)?
Which of the following correctly compares the field inside a toroid with the field inside a solenoid?
A solenoid has length \(l = 0.5\) m, radius \(r = 1\) cm \(= 0.01\) m, total turns \(N = 500\), and carries current \(I = 5\) A. What is the turns per unit length?
