The starter motor of a car engine draws an electric current of 110 A from the battery. The copper wire to the motor is 4.20 mm in diameter and 1.73 m long. The starter motor runs for 0.95 s before the car engine starts up.

How much electric charge passes through the starter motor?
________
What is the current density in the wire?
_________
How far does an electron travel along the wire while the starter motor is on? (The density of conduction electrons in copper is n = 8.50×1028 1/m3.)
________

Answer:

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

Explanation:

a. How much electric charge passes through the starter motor?

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

b. What is the current density in the wire?

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

c. How far does an electron travel along the wire while the starter motor is on? (The density of conduction electrons in copper is n = 8.50×1028 1/m3.)

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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