Question

Q) we want to calculate how long it takes for an electron to get from a car battery to the starter motor after the ignition switch is turned. assume that the current flowing is 115 a, and that the electrons travel through copper wire with cross-sectional area 31.2 mm² and length 85.5 cm. what is the current density in the wire? The number density of the conductor electrons in copper is 8.49 × 10²⁸/m³. Given this number density and the current density, what is the drift speed of the electrons? How long does it take for an electron starting at the battery to reach the starter motor? Assume no collision.

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Answer 1

Answer:

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Explanation:

Answer 2

Answer:

a. 104.5 C b. 7.94 × 10⁶ A/m² c. 5.83 × 10⁻⁴ m/s

Explanation:

Step 1: When retained in an electric or magnetic field, matter's fundamental physical attribute, electric charge, exerts a force. A moving electric charge creates a magnetic field, and an electric charge is related with an electric field. The electromagnetic field is made up of both electric and magnetic fields. The electromagnetic force, the cornerstone of physics, is produced by the interaction of the charges.

Using Q = It where Q = electric charge passing through the starter motor, I = current = 110 A and t = time = 0.95 s

So, Q = It = 110 A × 0.95 s = 104.5 C

Step 2: The current density, J = I/A where I = current = 110 A and A = cross-sectional area = πd²/4 where d = diameter of copper wire = 4.20 mm = 4.20 × 10⁻³ m

So, J = I/A

= I/πd²/4

= 4I/πd²

= 4 × 110 A/π(4.20 × 10⁻³ m)²

= 440 A/55.42 × 10⁻⁶ m²

= 7.94 × 10⁶ A/m²

Step 3: To find how far the electron travels, we need to find the electron drift velocity from

J = nev where J = current density = 7.94 × 10⁶ A/m², n = electron density = 8.50 × 10²⁸ m⁻³, e = electron charge = 1.602 × 10⁻¹⁹ C, v = drift velocity of electrons and A = cross-sectional area of wire = πd²/4 where d = diameter of copper wire = 4.20 mm = 4.20 × 10⁻³ m

So, v = J/ne

Substituting the values of the variables into the equation, we have

v = 7.94 × 10⁶ A/m² ÷ (8.50 × 10²⁸ m⁻³ × 1.602 × 10⁻¹⁹ C)

v = 7.94 × 10⁶ A/m² ÷ (13.617 × 10⁹ Cm⁻³)

v = 0.583 × 10⁻³ m/s

v = 5.83 × 10⁻⁴ m/s

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