Question

A very long wire carries a uniform linear charge density λ. Using a voltmeter to measure potential difference, you find that when one probe of the meter is placed 2.30 cm from the wire and the other probe is 1.50 cm farther from the wire, the meter reads 550 V . A) What is |λ|?

B) If you now place one probe at 3.30 cm from the wire and the other probe 1.50 cm farther away, will the voltmeter read 550 V , more or less than 550 V ?

Answer 1

To find the linear charge density of a long wire, use the formula |λ| = (V / ln(d2 / d1)), where V is the potential difference and d1 and d2 are the distances of the probes from the wire. For the given values, |λ| is approximately 198.4 V. If the distances between the probes change, the voltmeter will read less than 550 V.

Step-by-step explanation:

To find the linear charge density, we can use the formula:

|λ| = (V / ln(d2 / d1))

where V is the potential difference, d1 is the distance of the first probe from the wire, and d2 is the distance of the second probe from the wire.

Substituting the given values, we have:

|λ| = (550 V / ln((1.5 cm + 2.3 cm) / 2.3 cm)) = 275 V / ln(2)

Therefore, |λ| ≈ 198.4 V.

If one probe is placed at 3.30 cm from the wire and the other probe is placed 1.50 cm farther away, the voltmeter will read less than 550 V. As the distance between the probes increases, the potential difference decreases.