1. A very thin rod has positive charge uniformly distributed over length W. We want to find electric field at a point a distance & from the right end of the rod. To find the electric field we need to break up the rod into very small pieces. The pieces are so small that we can use the point charge formula for the E field due to each piece. Each small piece is a different distance from the point P so it will contribute a different amount to the total electric field. We need an integration variable which describes where each piece is. To do so we make the following steps. W dx 1+Q L dE a. Choose an integration variable. You can call it anything you like except that you cannot use the given symbols in the problem (W, L). Here we call our integration variable x. b. Choose a representative small piece on the rod. This piece represents all the pieces of the rod so do NOT choose a special piece such as the end of the rod or the exact middle. c. Choose and label the origin for your integration variable and the distance from the origin to the small piece. d. Draw the little bit of electric field de due to the small piece that you picked. e. Determine dE in terms of givens Q, W and/or L, the integration variable x, and the length of small piece dq.
1. A very thin rod has positive charge uniformly distributed over length W. We want to find electric field at a point a distance & from the right end of the rod. To find the electric field we need to break up the rod into very small pieces. The pieces are so small that we can use the point charge formula for the E field due to each piece. Each small piece is a different distance from the point P so it will contribute a different amount to the total electric field. We need an integration variable which describes where each piece is. To do so we make the following steps. W dx 1+Q L dE a. Choose an integration variable. You can call it anything you like except that you cannot use the given symbols in the problem (W, L). Here we call our integration variable x. b. Choose a representative small piece on the rod. This piece represents all the pieces of the rod so do NOT choose a special piece such as the end of the rod or the exact middle. c. Choose and label the origin for your integration variable and the distance from the origin to the small piece. d. Draw the little bit of electric field de due to the small piece that you picked. e. Determine dE in terms of givens Q, W and/or L, the integration variable x, and the length of small piece dq.
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part a,b,c,d,e please if you cannot answer all the parts, then my priority is part e.
Transcribed Image Text:1. A very thin rod has positive charge uniformly distributed over length W. We want to find electric field at a point a
distance & from the right end of the rod.
To find the electric field we need to break
up the rod into very small pieces. The
pieces are so small that we can use the
point charge formula for the E field due to
each piece.
Each small piece is a different distance from
the point P so it will contribute a different
amount to the total electric field. We need
an integration variable which describes
where each piece is. To do so we make the
following steps.
0
W
dx
|+Q
L
P
dE
a. Choose an integration variable. You can call it anything you like except that you cannot use the given symbols
in the problem (W, L). Here we call our integration variable x.
b. Choose a representative small piece on the rod. This piece represents all the pieces of the rod so do NOT
choose a special piece such as the end of the rod or the exact middle.
c. Choose and label the origin for your integration variable and the distance from the origin to the small piece.
d. Draw the little bit of electric field de due to the small piece that you picked.
i.
e. Determine dE in terms of givens Q, W and/or L, the integration variable x, and the length of small piece dq.
Determine dq: da is the charge in the small piece dx. We want to write da in terms of givens and dx. Hint:
the charge is distributed uniformly over the length of the rod so the charge per length A is constant. Write
the charge per length two ways: (1) using the total charge Q and the total length W, and (2) using the small
charge dq and small length dx. Set the two expressions for equal to each other and solve for da. Check
that your expression for da has the correct dimensions: Note that dx is a little bit of length sohas Si units of
meters.
dq
Units for dq (show work):
What is the distance from the point P to the small piece? Write in terms of givens L and/or W and the
integration variable x. Note dx is very small so you can ignore it in determining the distance r.
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