Brad_1234
Dec13-05, 02:34 PM
Its from an example in the book, and it doesnt seem to make sense,
A rod of length l has a uniform positive charge per unit length (lambda) and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end.
So then the example takes a small part of the rod, dx which has charge of dq, and is distance x from point P.
dq = (lambda)dx and dE = ke dq/x^2 or ke lambda dx / x^2
fine so far.
Now the example says we must sum up the contributions of all the segments.
it becomes an integral E = (integral) from a to l+a of ke lambda dx/x^2
the example breaks the dq component out into ke lambda [ - 1/x ] from a to l+a Im somewhat confused now.
then it goes on, ke lambda(1/a - 1/l+a) = keQ/a(l+a) ??? what??!!
okay it kind of makes sense, the total charge divided by length, but the last part there is a divide by zero error to my thought process, multiplying an item with example values: Lambda(1/a - 1/b) or Q/l(1/a - 1/b) might give (Q/l * 1/a) - (Q/l * 1/b) if doing the same thing for the actual values, should give Q/la - Q/la + l^2 ?? no?
reducing it down to Q/a(a+l) ? the book doesnt explain how it arrived at this.
Can anyone give an example of calculating the Field from a charged rod? apparently its the same in a ring from the x axis but using vectors, but this concept seems tough, thanks for any explanations
A rod of length l has a uniform positive charge per unit length (lambda) and a total charge Q. Calculate the electric field at a point P that is located along the long axis of the rod and a distance a from one end.
So then the example takes a small part of the rod, dx which has charge of dq, and is distance x from point P.
dq = (lambda)dx and dE = ke dq/x^2 or ke lambda dx / x^2
fine so far.
Now the example says we must sum up the contributions of all the segments.
it becomes an integral E = (integral) from a to l+a of ke lambda dx/x^2
the example breaks the dq component out into ke lambda [ - 1/x ] from a to l+a Im somewhat confused now.
then it goes on, ke lambda(1/a - 1/l+a) = keQ/a(l+a) ??? what??!!
okay it kind of makes sense, the total charge divided by length, but the last part there is a divide by zero error to my thought process, multiplying an item with example values: Lambda(1/a - 1/b) or Q/l(1/a - 1/b) might give (Q/l * 1/a) - (Q/l * 1/b) if doing the same thing for the actual values, should give Q/la - Q/la + l^2 ?? no?
reducing it down to Q/a(a+l) ? the book doesnt explain how it arrived at this.
Can anyone give an example of calculating the Field from a charged rod? apparently its the same in a ring from the x axis but using vectors, but this concept seems tough, thanks for any explanations