A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to the axis; both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? g = 9.8 ms^–2.

Solution

Given a solenoid.
Length of the solenoid,l = 60 cm = 0.60 m
Total number of turns, N = 3 x 300 = 900
Length of the wire, l₁ = 2.0 cm = 0.02 m
mass of the wire lying inside the solenoid,m 2.5 g = 2.5 x 10^–3 kg
Current carried by the wire,I₁ = 6.0 A

Let, current I be passed through the solenoid windings, then,
Magnetic field produced inside the solenoid due to current is

$B = \frac{μ_{0} NI}{l}$

Force acting on wire, $= I_{1} l_{1} B = I_{1} l_{1} \frac{μ_{0} NI}{l}$

The wire can be supported if the force on wire is equal to the weight of wire, i.e.

$I_{1} l_{1} \frac{μ_{0} NI}{l} = mg$

$\Rightarrow$ $I = \frac{mg l}{I_{1} l_{1} μ_{0} N} = \frac{2.5 \times 10^{- 3} \times 9.8 \times 0.6}{(6.0) \times (0.02) \times (4 π \times 10^{- 7})} \times 900$

$= 108.27 A$

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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