Part A: Find the potential P, a distance x to the right of the rod. Express your

Question

Part A: Find the potential P, a distance x to the right of the rod.

Express your answers in terms of the given quantities and appropriate constants.

V = ?

Part B: Find the potential point R, a distance y above the right-handed side of the rod.

Express your answers in quantities and constants.

Part C: In part A, what does your result reduce to as x becomes much larger than a?

Express your answers in quantities and constants.

Part D: In part B, what does your result reduce to as y becomes much larger than a?

Express your answers in quantities and constants.

Explanation / Answer

a) consider a random cut dx with charge dq that will produce little dV dV= k dq/r dq = Q dx/a so dV = k Q/a dx/x integrate both sides right side varies from x=x to x+a V= kQ/a ln x from x to x+a V = kQ/a ln( (x+a)/x) V= kQ/a ln (1 +a/x) b) similar except now r = sqrt(y^2 + x^2) and x varies from to a so dV = kQ/a dx/sqrt(y^2+x^2) V = kQ/a arcsinh( a/y) c) if x>a then a/x is small then ln(1+a/x) is approximately a/x so V= kQ/a (a/x) = kQ/x so behaves like point charge d) if y>a then a/y is small arcsinh is approximately a/y so V= kQ/y

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects