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Now apply the equations 1, 2 and 3 above to calculate the emf induced in a solenoid. From the experiment, the solenoid tube we used has an internal diameter of about 4cm. It has windings of about 519 turns and carries a current of 50mA. What is B at its centre? If you were to replace the magnetic bar with a smaller solenoid tube of 100 turns (has its own electric field) and having a diameter of Icm, it can also act as a magnet, because it will have its own electric field. When you place the smaller tube in, there will be an induced emf (e) in the larger tube. What is this induced emf (E)? ​

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ajeigbeibraheem

By applying the equation 1, 2, and 3, the induced emf (E) in a solenoid is 12.32 J/C.

Given that:

  • the number of turns (N) in the solenoid tube = 519 turns
  • the diameter of the turn = 4 cm = 4 × 10⁻²

Applying the equation for the length of the solenoid as equation (1);

  • Length = N × D
  • L = 519 × 4 × 10⁻²
  • L = 20.76 m

The magnetic B from the center can be estimated by applying the equation (2);

Using the equation or magnetic field B;

[tex]\mathbf{B = \dfrac{\mu_o \times N \times I}{l}}[/tex]

where;

  • [tex]\mathbf{\mu_o =}[/tex] permeability of free space = 4π × 10⁻⁷
  • current (I) = 50 mA = 5.0 × 10⁻³ A
  • length of the solenoid (l) = 20.76

∴

[tex]\mathbf{B = \dfrac{4 \pi \times 10^{-7}\times 519 \times 50 \times 10^{-3}}{20.76}}[/tex]

B = 1.57 × 10⁻ T

B = 1.57 μT

Finally, applying equation (3) for the induced emf, the induced emf can be calculated by using the formula:

[tex]\mathbf{\varepsilon = \dfrac{n \times B\times A}{\Delta t}}[/tex]

where;

  • the number of turns (n) of the small solenoid = 100
  • Area A = πr²
  • Area A = π × (0.5 × 10⁻²)² = 7.85 × 10⁻⁵

[tex]\mathbf{\varepsilon = \dfrac{100 \times 1.57 \times 10^{-6}\times 7.85 \times 10^{-5}}{1}}[/tex]

[tex]\mathbf{\varepsilon =1.232 \times 10^{-8} \ v/s}[/tex]

  • Since 1 volt per second = 1 Joules/ Columb.

∴

The induced emf [tex]\mathbf{\varepsilon =12.32 \times 10^{-9} \ J/C}[/tex]

Learn more about the Electric field here:

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