{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Extra expanding the result 3 in powers of ar 1 and

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , Ex,upper = (R-a/2)3 and Ex,lower = -ke qa , while their total is just (4). (R+a/2)3 Compared to the field of a point charge, which falls off with distance R as R-2 , and of a dipole, which falls off as R-3 , the field of our system falls off faster, as R-4 . This is because both total charge and total dipole moment are zero in this case, our system is what is called (an elementary) quadrupole. 1 2. The field of the infinite line at distance x from it is E(x) = 2ke /x. The force acting on a small element dx of the rod is E(x)(Q/2a)dx, the total force therefore is just r+a r+a ke Q ln . (5) F = E(x)(Q/2a)dx = a r-a r-a When r a, this expression turns into F = 2ke Q/r, as one should expect (the rod looks like a point charge). 3. The electric field E(r) =...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online