Consider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to > = -f, where is a unit vector directed radially outward 2περτ λ this line of charge is given by E = 2k, T from the infinitely long wire of charge. Hint a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to this infinite line of charge at some distance r from the line of charge. Give your answer in terms of given quantities (A.ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for V(r) calculation V(r) b. There is a reason we are not setting V(r→ ∞o) = 0 as we normally do (in fact, in general, whenever you have an infinite charge distribution, this "universal reference" does not work; you need a localized charge distribution for this reference to work). Which of the following best describes what happens to potential as roo? (That is, what is V(r→∞o), with our current reference, V(ro) = 0?) OV(r→ ∞o) asymptotically approaches a finite value. OV(ro) decreases to -∞o without limit. OV(r→∞o) increases to +∞o without limit. OV(ro) oscillates within a bounded range (no well-defined limit but does not diverge).
Consider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to > = -f, where is a unit vector directed radially outward 2περτ λ this line of charge is given by E = 2k, T from the infinitely long wire of charge. Hint a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to this infinite line of charge at some distance r from the line of charge. Give your answer in terms of given quantities (A.ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for V(r) calculation V(r) b. There is a reason we are not setting V(r→ ∞o) = 0 as we normally do (in fact, in general, whenever you have an infinite charge distribution, this "universal reference" does not work; you need a localized charge distribution for this reference to work). Which of the following best describes what happens to potential as roo? (That is, what is V(r→∞o), with our current reference, V(ro) = 0?) OV(r→ ∞o) asymptotically approaches a finite value. OV(ro) decreases to -∞o without limit. OV(r→∞o) increases to +∞o without limit. OV(ro) oscillates within a bounded range (no well-defined limit but does not diverge).
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Transcribed Image Text:Consider an infinitely long wire of charge carrying a positive charge density of A. The electric field due to
1
this line of charge is given by E = 2k,
= -, where is a unit vector directed radially outward
2πεor
T
from the infinitely long wire of charge.
Hint
#3
3
a. Letting the voltage be zero at some reference distance (V(ro) = 0), calculate the voltage due to
this infinite line of charge at some distance r from the line of charge. Give your answer in terms of
given quantities (A,ro,r) and physical constants (ke or Eo). Use underscore ("_") for subscripts and
spell out Greek letters.
Hint for V(r) calculation
V(r) =
b. There is a reason we are not setting V(r→ ∞o) = 0 as we normally do (in fact, in general,
whenever you have an infinite charge distribution, this "universal reference" does not work; you need
a localized charge distribution for this reference to work).
Which of the following best describes what happens to potential as roo? (That is, what is
V(ro), with our current reference, V(ro) = 0?)
OV(ro) asymptotically approaches a finite value.
OV(→ ∞) decreases to -∞o without limit.
OV(ro) increases to +∞o without limit.
OV(roo) oscillates within a bounded range (no well-defined limit but does not diverge).
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