Background Info When a power source like a battery is connected to a circuit, an

Question

Background Info

When a power source like a battery is connected to a circuit, an electric field pushes electrons within the conducting wires causing them to flow. The electric field exists due to an uneven build up of charge on the surfaces of the wires (called a surface charge gradient). In this set of problems we will explore a simple model of how this all comes about and emphasize the connection between source charges, electric fields, and voltage differences in the context of electric circuits.

A very small segment of the conducting wire in a circuit can be modeled as a circular ring of radius 0 mm. Consider two such rings surrounding the z-axis separated by a small distance 1 mm. Let's first suppose that both rings have the same charge density. What is the strength of the electric field on the z-axis at the midpoint between the two rings?

Correct, computer gets: 0 V/m

19[E]) If you used a voltmeter to measure the voltage difference between the centers of the two rings, what measurement would you read?

Correct, computer gets: 0 V

My Question

Now suppose that a power source is plugged into the circuit and that after a brief moment, you measure the voltage difference between the centers of the two rings to be 2 mV. What is the difference between the charge densities on the two rings?

Explanation / Answer

electric field and Electric potential are related by E = V/d

so

E = 2 e -3/1 e -3 = 2 N/C

so as Electric field E = sigma/2eo

sigam = 2 E eo

sigma = 2* 2 * 8.85 e -12

sigma = charge density = 3.54 e -11 C/m^2

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.