GREPhysics.NET: GR9677 #3

GR9677 #3

Problem

GREPhysics.NET Official Solution

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Electromagnetism $\Rightarrow$ }Potential

Recall the elementary equations, $V = \int \vec{E}\cdot d\vec{l} = \int \frac{dq}{4\pi \epsilon_0 r}$ .

$r=\sqrt{R^2+x^2}$ , and $dQ=Q$ thus $V=\frac{Q}{4\pi \epsilon_0 \sqrt{R^2+x^2}}$ , as in choice (B).

Alternate Solutions

jmason86 2009-09-28 18:37:55	Don't even both with anything more than the distance. All the answers are identical except for the dependence on R and x which are the distances. You know that $V\prop \frac{1}{r}$ so just get r. Draw the triangle and see that (B) does the job. Reply to this comment
spacebabe47 2007-09-19 13:39:58	As R -> 0, the equation should simplify to the potential for a point charge. This eliminates C, D and E. The equation should also have some R dependence, this eliminates A. Choose B. Reply to this comment
sblusk 2006-10-24 06:14:40	An alternate way would be to just use directly: V(r) = Integral (1/4(pie_0))* dQ/r where r=sqrt(R^2+x^2). This is in principle easier because one is dealign with a scalar, and not the electric field which is a vector. Reply to this comment

Comments

jmason86
2009-09-28 18:37:55

Don't even both with anything more than the distance. All the answers are identical except for the dependence on R and x which are the distances. You know that $V\prop \frac{1}{r}$ so just get r.

Draw the triangle and see that (B) does the job.

Reply to this comment

spacebabe47
2007-09-19 13:39:58

As R -> 0, the equation should simplify to the potential for a point charge. This eliminates C, D and E. The equation should also have some R dependence, this eliminates A. Choose B.

ewhite2
2007-10-30 17:32:36

how is C eliminated?

kyros
2007-11-01 10:40:09

C isn't eliminated that way -but it's clear that at x = 0, the answer should be non-zero(consider a positive charge and positive Q, the integral from infinity to zero can't be zero.)

Reply to this comment

sblusk
2006-10-24 06:14:40

An alternate way would be to just use directly:

V(r) = Integral (1/4*(pi*e_0))* dQ/r

where r=sqrt(R^2+x^2).

This is in principle easier because one is dealign with a scalar, and not the electric field which is a vector.

Reply to this comment

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