course phy 202
11:25 4/13/10
023.
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Question: `qIn your own words explain how the introductory experience with scotch tape illustrates the existence of two types of charge.
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Your Solution:
It was like the two pieces of tape, after ripping them apart, were magnetic (in the sense that they had poles). This was caused by the tow different charges on the tape, positive and negative.
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Question: `qIn your own words explain how the introductory experience with scotch tape supports the idea that the force between two charged particles acts along a straight line through those particles, either attracting the forces along this line or repelling along this line.
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Your Solution:
The tape attracts on one side but repels on the other. I guess the line would be the centerline of the thickness on the tape.
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Question: `qIn your own words explain why this experience doesn't really prove anything about actual point charges, since neither piece of tape is confined to a point.
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Your Solution:
You cannot tell exactly where the charge is coming from, you just know it is from this side of the tape.
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Question: `qIf one piece of tape is centered at point A and the other at point B, then let AB_v stand for the vector whose initial point is A and whose terminal point is B, and let AB_u stand for a vector of magnitude 1 whose direction is the same as that of AB_u. Similarlylet BA_v and BA_u stand for analogous vectors from B to A. Vectors of length 1 are called unit vectors. If the pieces attract, then in the direction of which of the two unit vectors is the tape at point A pushed or pulled? If the pieces repel, then in the direction of which of the two unit vectors is the tape at B pushed or pulled? Explain.
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Your Solution:
They would pull towards each other in the opposite direction they were pulled apart.
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Question: `qUsing the notation of the preceding question, which you should have noted on paper (keep brief running notes as you do qa's and queries so you can answer 'followup questions' like this), how does the magnitude of the vector AB_v depend on the magnitude of BA_v, and how does the magnitude of each vector compare with the distance between A and B?
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Your Solution:
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Question: `qUsing the notation of the preceding question, how is the force experienced by the two pieces of tape influenced by the magnitude of AB_v or BA_v?`aThe expected answer is that the force exerted by two charges on one another is inversely proportional to the square of the distance between them. So as the magnitudes of the vectors, which are equal to the separation, increases the force decreases with the square of the distance; and/or if the magnitude decreases the force increases in the same proportinality. The two pieces of tape are not point charges, so this is not strictly so in this case, as some parts of the tape are closer than to the other tape than other parts.
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Your Solution: AB_v/(AB_v)absolute value
So AB_u would either be 1 or -1.
AB_u and BA_v are vectors, so they have both magnitude and direction. In one dimension direction can be specified by + and - signs. In two dimensions + and - signs are not sufficient, and the direction direction of a vector is generally specified by the angle as measured counterclockwise from the positive x axis.
The magnitude of AV_u would be the same as that of VA_u, but would be in the opposite direction.
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STUDENT COMMENT: Still not sure how to answer this question. I dont know what sort of difference there is between the magnitude vector and the unit vector.
INSTRUCTOR RESPONSE: As noted in the preceding solution, AB_v stands for the vector whose initial point is A and whose terminal point is B, and AB_u stands for a vector of magnitude 1 whose direction is the same as that of AB_u.
To get a unit vector in the direction of a given vector, you divide that vector by its magnitude. So AB_u = AB_v / | AB_v |.
The purpose of a unit vector is to represent a direction. If you multiply a unit vector by a number, you get a vector in the same direction as the unit vector, whose magnitude is the number by which you multiplied it.
The problem does not at this point ask you to actually calculate these vectors. However, as an example:
Suppose point A is (4, 5) and point B is (7, 3). Then AB_v is the vector whose initial point is A and whose terminal point is B, so that AB_v = <3, -2>, the vector with x component 3 and y component -2.
The magnitude of this vector is sqrt( 3^2 + (-2)^2 ) = sqrt(11).
Therefore AB_u = <3, -2> / sqrt(11) = (3 / sqrt(11), -2 / sqrt(11) ). That is, AB_u is the vector with x component 3 / sqrt(11) and y component -2 / sqrt(11). (Note that these components should be written with rationalized denominators as 3 sqrt(11) / 11 and -2 sqrt(11) / 11, so that AB_u = <3 sqrt(11) / 11, -2 sqrt(11) / 11 > ). The vector AB_u is a unit vector: it has magnitude 1.
The unit vector has the same direction as AB_v. If we want a vector of magnitude, say, 20 in the direction of this vector, we simply multiply the unit vector AB_u by 20 (we would obtain 20 * <3 sqrt(11) / 11, -2 sqrt(11) / 11 > = <60 sqrt(11) / 11, -40 sqrt(11) / 11 >).
If you do not completely understand this by reading it here, you should of course sketch this situation and identify all these quantities in your sketch.
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Self-critique (if necessary):
Ok I think!!
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Self-critique rating #$&*1
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Question: `qQuery introductory set #1, 1-5
Explain how we calculate the magnitude and direction of the electrostatic force on a given charge at a given point of the x-y plane point due to a given point charge at the origin.
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Your solution:
Magnitude of force on a test charge Q is F = k q1 * Q / r^2, q1 is the charge at zero. The force is one repulsion if q1 and Q are the same sign, attraction if the signs are opposite.
confidence rating #$&*
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Given Solution:
`a** The magnitude of the force on a test charge Q is F = k q1 * Q / r^2, where q1 is the charge at the origin. The force is one of repulsion if q1 and Q are of like sign, attraction if the signs are unlike.
The force is therefore directly away from the origin (if q1 and Q are of like sign) or directly toward the origin (if q1 and Q are of unlike sign).
To find the direction of this displacement vector we find arctan(y / x), adding 180 deg if x is negative. If the q1 and Q are like charges then this is the direction of the field. If q1 and Q are unlike then the direction of the field is opposite this direction. The angle of the field would therefore be 180 degrees greater or less than this angle.**
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Self-critique (if necessary):
ok
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Self-critique rating #$&*2
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Question: `qExplain how we calculate the magnitude and direction of the electric field at a given point of the x-y plane due to a given point charge at the origin.
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Your solution:
The magnitude of the force on a test charge Q is F = k q1 * Q / r^2,
Q1= origin charge
The electric field is therefore F / Q = k q1 / r^2.
The electric field is either directly away from the origin (q1 greater than zero) or directly toward the origin (q1 less than zero).
Tan^-1 y/x
confidence rating #$&*
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Given Solution:
`a** The magnitude of the force on a test charge Q is F = k q1 * Q / r^2, where q1 is the charge at the origin.
The electric field is therefore F / Q = k q1 / r^2. The direction is the direction of the force experienced by a positive test charge.
The electric field is therefore directly away from the origin (if q1 is positive) or directly toward the origin (if q1 is negative).
The direction of the electric field is in the direction of the displacement vector from the origin to the point if q1 is positive, and opposite to this direction if q1 is negative.
To find the direction of this displacement vector we find arctan(y / x), adding 180 deg if x is negative. If q1 is positive then this is the direction of the field. If q1 is negative then the direction of the field is opposite this direction, 180 degrees more or less than the calculated angle. **
STUDENT QUESTION
Why is it just Q and not Q2?
INSTRUCTOR RESPONSE
q1 is a charge that's actually present. Q is a 'test charge' that really isn't there. We calculate the effect q1 has on this point by calculating what the force would be if a charge Q was placed at the point in question.
This situation can and will be expanded to a number of actual charges, e.g., q1, q2, ..., qn, at specific points. If we want to find the field at some point, we imagine a 'test charge' Q at that point and figure out the force exerted on it by all the actual charges q1, q2, ..., qn.
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Self-critique (if necessary):
ok
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Self-critique rating #$&*3
&#Good responses. See my notes and let me know if you have questions. &#