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Chapter 15: Q8Q (page 616)
Explain briefly how knowing the electric field of a ring helps in calculating the field of a disk.
Answer
The disk can be divided into tiny rings and the electric fields of the tiny rings can be added to get the electric field of the desk.
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Two rings of radius 4 cm are 12 cm apart and concentric with a common horizontal x axis. The ring on the left carries a uniformly distributed charge of , and the ring on the right carries a uniformly distributed charge of . (a) What is theelectric field due to the right ring at a location midway between the two rings? (b) What is the electric field due to the left ring at a location midway between the two rings? (c) What is the net electric field at a location midway between the two rings? (d) If a charge of were placed midway between the rings, what would be the force exerted on this charge by the rings?
If the magnitude of the electric field in air exceeds roughly 3 × 106 N/C, the air brake down and a spark form. For a two-disk capacitor of radius 47 cm with a gap of 1 mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)?
A disk of radius 16 cm has a total charge 4 × 10−6 C distributed uniformly all over the disk. (a) Using the exact equation, what is the electric field 1 mm from the center of the disk? (b) Using the same exact equation, find the electric field 3 mm from the center of the disk. (c) What is the percent difference between these two numbers?
A capacitor made of two parallel uniformly charged circular metal disks carries a charge of +Q and −Q on the inner surfaces of the plates and very small amounts of charge +q and −q on the outer surfaces of the plates. Each plate has a radius R and thickness t, and the gap distance between the plates is s. How much charge q is on the outside surface of the positive disk, in terms of Q?
A clear plastic pen 12 cmlong is rubbed all over with wool, and acquires a negative charge of . You want to figure out the electric field a distance of 18 mmfrom the pen, near the middle of the pen. (a) You decide to model the pen as a rod consisting of a series of five segments, each of which you will consider to be approximately point-like. What is the length of each segment in meters? (b) What is the amount of charge on each of the five segments? (c) In general, if the rod has a length Land total charge Q, and you divide the rod into Nsegments, what is the amount of chargeon each piece? (d) If the length of each segment is dL, write a symbolic expression for the number of pieces Nin terms of the length of the rod Land the length of one piece dL.(e) 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.
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