A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0A in 0.1 s, what is the induced emf in the loop while the current is changing?

Solution

Given, a solenoid.
Number of turns per unit length,n = 15 turns/cm = 1500 turns/m
Area of the small loop, A = 2 cm² = 2 x 10^–4 m²Initial current, I₁ = 2A
Final current, I₂ = 4A
Δt = 0.1s

The magnetic field associated with current I_1,

B_{1} = μ_{0} n I_{1}

The magnetic field associated with current

I_{2},

B_{2} = μ_{0} n I_{2}

The change in flux assosciated with change in current in solenoid,

∆ ϕ = (B_{2} - B_{1}) A = 4 π \times 10^{- 7} \times 1500 \times (4 - 2) \times 2 \times 10^{- 4}

= 7.6 \times 10^{- 7} weber

The induced EMF while current is changing,

|E| = \frac{∆ ϕ}{∆ t} = \frac{7.6 \times 10^{- 7}}{0.1} = 7.6 \times 10^{- 6} V

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Electric Charges And Fields

A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0A in 0.1 s, what is the induced emf in the loop while the current is changing?

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0A in 0.1 s, what is the induced emf in the loop while the current is changing?

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0A in 0.1 s, what is the induced emf in the loop while the current is changing?

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?