A very long wire carries a uniform positive linear charge density lambda. Using
ID: 1424186 • Letter: A
Question
A very long wire carries a uniform positive linear charge density lambda. Using a voltmeter to measure potential difference, you find that when one probe of the meter is placed 2.69 cm from the wire and the other probe is 1.00 cm farther from the wire, the meter reads a magnitude of 567 V. Concept: Which probe of the voltmeter will be at a lower voltage? If the probes were both moved radially 3 cm further from the wire (but still kept the same 1 cm distance apart), the voltmeter reading would: Calculate: What is lambda? If you place both probes 3.50 cm from the wire but 16.6 cm from each other, what will the voltmeter read? Also: Sketch an electric field map of the region. Include some equipotentials, and note their spacing. Contemplate if/where you could set V=0 for this non-finite charge distribution. A very long wire carries a uniform positive linear charge density lambda. Using a voltmeter to measure potential difference, you find that when one probe of the meter is placed 2.69 cm from the wire and the other probe is 1.00 cm farther from the wire, the meter reads a magnitude of 567 V. Concept: Which probe of the voltmeter will be at a lower voltage? If the probes were both moved radially 3 cm further from the wire (but still kept the same 1 cm distance apart), the voltmeter reading would: Calculate: What is lambda? If you place both probes 3.50 cm from the wire but 16.6 cm from each other, what will the voltmeter read? Also: Sketch an electric field map of the region. Include some equipotentials, and note their spacing. Contemplate if/where you could set V=0 for this non-finite charge distribution.Explanation / Answer
Electric field due to a line of charge = E=2k*lembda/r
dU = -Edr= -(2k*lembda/r)dr
Potential difference = U2-U1 = integral -(2k*lembda/r)dr
U2 - U1 = -(2k*lembda)ln(r2/r1)
r1 =2.69 cm
r2 =1.0 cm
U2 - U1 = -567 V
-(2k*lembda)ln(r2/r1)=U2 - U1
lembda=-567 /(-2*9*10^9)ln(2.69/1.0)
lembda= 31.5*10^-9/ln(2.69/1.0)
lembda= 3.183*10^-8 C/m^2
i) the absolute value of Lambda is 3.183*10^-8 C/m^2
ii)
The voltmeter read zero because the two points are at same potential.