PHYS 212 Chapter 26: 26.4-26.7

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26 Feb 2017

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26. 4: the e-fields of rings, disks, planes, and spheres. R is the radius of the ring. Z is the distance from the center of the ring perpendicular to. (cid:4666)(cid:3045) (cid:3047)(cid:4667)= (cid:2869)4 0 (cid:3018) (cid:4666)(cid:3118)+(cid:3019)(cid:3118)(cid:4667)(cid:3119)/(cid:3118)works for both positive and negative z. Divide disk into infinitely many rings with radius ri and charge (cid:1843) On axis electric field of a charged disk is increases out to about |z| = r, then decreases again. Disks factor z^2 out of the square root to get (cid:4666)(cid:3031)(cid:3046)(cid:3038)(cid:4667)= (cid:884)(cid:2868)[(cid:883) (cid:4666)(cid:3031)(cid:3046)(cid:3038)(cid:4667)= (cid:884)(cid:2868)[(cid:883) . Electrodes can often be modeled as infinite planes. Electric field of a plane of charge is found from a disk of infinite radius. Positively charged planes have electric fields pointing away on both sides. So, if z is less than zero, the field must be inverted. 26. 5: the parallel plate capacitor two electrodes equally oppositely charged find between plates (inside) and outside the capacitor.

Related Questions

Consider two thin disks of negligible thickness, of radius R perpendicular to the x-axis such that the x-axis runs through the center of each disk. The disk centered at x=0 has a positive charge density and the disk centered at x=a has a negative charge density , where charge density is the charge per unit area.

What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2?

ceruleanwasp805

Step 1:

Since we know the electric field of a charged ring, divide thetube into rings, of thickness dx. Consider arepresentative ring somewhere in the middle of the tube, with itscenter at . Draw a diagram illustrating this situation.

Step 2:

(a) How much charge dQ is on this ring? Write youranswer symbolically. (Use any variable or symbol stated above asnecessary.)

dQ = ________

(b) What is the distance from this ring to the observationlocation?

d = ________

r = ________ (this answer is a vector)

(d) What is the integration variable? (Use any variable orsymbol stated above as necessary.)

answer = ________

(e) What is the lower integration limit? (Use any variable orsymbol stated above as necessary.)

answer = ________

(f) What is the upper integration limit? (Use any variable orsymbol stated above as necessary.)

answer = ________

Step 3:

Evaluate the integral, using the tool of your choice.

Step 4:

Check the units, and the special case where w>>R.

A thin-walled hollow circular glass tube, open at both ends, has aradius R and length L (see the figure). The axis of the tube liesalong the x axis, with the left end at the origin. The outer sidesare rubbed with silk and acquire a net positive charge Qdistributed uniformly. Determine the electric field at a locationon the x axis, a distance w from the origin. Carry out all stepsincluding checking your result. Explain each step. You may have torefer to a table of integrals.

Step 1:
Since we know the electric field of a charged ring, divide the tubeinto rings, of thickness dx. Consider a representative ringsomewhere in the middle of the tube, with its center at . Draw adiagram illustrating this situation.

Step 2:
(a) How much charge dQ is on this ring? Write your answersymbolically. (Use any variable or symbol stated above asnecessary.)

dQ = ________

(b) What is the distance from this ring to the observationlocation?

d = ________

(c) What is the vector from the source to observationlocation?

r = ________ (this answer is a vector)

(d) What is the integration variable? (Use any variable or symbolstated above as necessary.)

answer = ________

(e) What is the lower integration limit? (Use any variable orsymbol stated above as necessary.)

answer = ________

(f) What is the upper integration limit? (Use any variable orsymbol stated above as necessary.)

answer = ________

Step 3:
Evaluate the integral, using the tool of your choice.

Step 4:
Check the units, and the special case where w>>R.

PHYS 212 Chapter 26: 26.4-26.7

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