Question

A 510-turn solenoid has a radius of 8.00 mm and an overall length of 14.0 cm. (a) What is its inductance? (b) If the solenoid is connected in series with a 2.50-?(ohm electrical symbol) resistor and a battery, what is the time constant of the circuit?

Answer 1

Step 1:

Definition:

Inductance: is the property of a conductor by which a change in current flowing through it induces (creates) a voltage (electromotive force) in both the conductor itself (self-inductance), and in any nearby conductors (mutual inductance).

These effects are derived from two fundamental observations of physics: First, that a steady current creates a steady magnetic field (Oersted's law), and second, that a time-varying magnetic field induces voltage in nearby conductors (Faraday's law of induction). According to Lenz's law, a changing electric current through a circuit that contains inductance induces a proportional voltage, which opposes the change in current (self-inductance). The varying field in this circuit may also induce an e.m.f. in neighbouring circuits (mutual inductance).

Step 2:

A solenoid is a long, thin coil, i.e. a coil whose length is much greater than the diameter. Under these conditions, and without any magnetic material used, the magnetic flux density within the coil is practically constant and is given by

where is the magnetic constant, the number of turns, the current and the length of the coil. Ignoring end effects, the total magnetic flux through the coil is obtained by multiplying the flux density by the cross-section area :

When this is combined with the definition of inductance,

it follows that the inductance of a solenoid is given by:

Step 3:

(a) What is its inductance?

ANSWERS:

Carry 14 centimeters to meters

Carry 8 milimeters to meters

(b) If the solenoid is connected in series with a 2.50 (ohm electrical symbol) resistor and a battery, what is the time constant of the circuit?

The time constant for circuit R-L is:

  

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