A clear plastic pen 12 cm long is rubbed all over with wool, and acquires a nega

Question

A clear plastic pen 12 cm long is rubbed all over with wool, and acquires a negative charge of -5 nanocoulombs. You want to figure out the electric field a distance of 17 mm from the pen, near the middle of the pen.

(a) You decide to model the pen as a rod consisting of a series of 5 segments, each of which you will consider to be approximately point-like. What is the amount of charge Q on each of the 5 segments? (Substitute numeric values, do not use variables.)

Delta Q = C per segment

(b) In general, if the rod has a length L and total charge Q, and you divide the rod into N segments, what is the amount of charge Q on each piece? Write a symbolic expression. Use the following as necessary: Q, L, and N.

Delta Q =

(c) If the length of each segment is dL, write a symbolic expression for the number of pieces N in terms of the length of the rod L and the length of one piece dL. Use the following as necessary: Q, L, and dL.

N =

(d) Now write a symbolic expression for the amount of charge on each piece in terms of the length of the rod and the length of a small piece. Use the following as necessary: Q, L, and dL.

Delta Q =

Explanation / Answer

part a:

charge on each segment=total charge/number of segments=-5 nC/5=-1 nC

part b:

length of each segment=L/N

charge per unit length=Q/L

then charge on each segment=(L/N)*(Q/L)=Q/N

as there are N segments, charge on each segment=Q/N

part c:

length of each segment is dL, total length is L,

then number of segments=total length/length of each segment

==>N=L/dL

part d:

from part b,

charge on each segment=Q/N

from part c, N=L/dL

then charge on each segement=Q/(L/dL)=Q*dL/L

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