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# webct11 - 4 corners 1. Three charges Q1, Q2 and Q3 are...

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4 corners 1. Three charges Q 1 , Q 2 and Q 3 are pinned at three of the corners of a square of side a . A fourth charge q is gently placed on the fourth corner. It is observed that there is no net force acting on it. Assume that Q 1 < 0. Which of the following relations is true? a. | Q 2 | = | Q 3 | and Q 2 , Q 3 < 0 b. | Q 2 | > | Q 3 | and Q 2 , Q 3 < 0 c. | Q 2 | < | Q 3 | and Q 2 , Q 3 < 0 *d. | Q 2 | = | Q 3 | and Q 2 , Q 3 > 0 e. | Q 2 | > | Q 3 | and Q 2 , Q 3 > 0 f. | Q 2 | < | Q 3 | and Q 2 , Q 3 > 0 Let us assume q > 0. Then, since charge Q 1 < 0, the force by this charge will be attractive and as shown below: F 1

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For the total force to be zero, we will therefore need the forces due to Q 2 and Q 3 to have a resultant that points exactly in the opposite direction. To achieve this, we need these two forces to be repulsive, so Q 2 > 0 and Q 3 > 0, and they must have the same magnitude (otherwise the resultant would not point at 45º), and thus Q 2 = Q 3 If we start by assuming q < 0, the reasoning is identical, except the force by Q 1 is repulsive and the forces by Q 2 and Q 3 are attractive. 2. Find the ratio Q 1 / Q 2 . For q > 0, these are the three forces acting on q : Their magnitudes are: 1 1 2 2 23 2 2 qQ Fk a FFk a = == Let us add F 2 and F 3 first: 2 22 2 3 2 2 FF F F k a += + = G G This must be equal to the magnitude of F 1 : F 1 F 2 F 3
12 3 22 1 2 2 2 2 2 2.83 FF F qQ kk aa Q Q =+ = == GG G 3. The fourth charge ( q ) is replaced by one with opposite sign but same magnitude (i.e., q ). The new charge: a. Is sucked towards Q 1 . b. Is sucked towards Q 2 . c. Is sucked towards Q 3 . d. Is pushed away. *e. Does not move. The electric force on a charge – q has the same magnitude and opposite direction than the electric force on a charge + q . So the net force is still zero and the charge does not move.

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2 spheres 1. Two small, identical, pointlike conducting spheres have charges q 1 = -2 μC and q 2 = +8 μC. Find the magnitude of the electrical force between them when they are separated by 25 cm. The magnitude of the electrical force between two point like charges q 1 and q 2 seperated by distance R is given by Coulomb’s law () ( ) 66 2 12 9 2 22 2 2 10 C 8 10 C Nm 9 10 2.3 N C 25 10 m qq Fk R −− ××  == × =   × 2. The forces are: *a. Attractive. b. Repulsive. Since the charges are opposite in sign and the opposite charges attract each other, the forces are attractive. 3. The two spheres are brought momentarily into contact and then separated again by a distance of 25 cm. What is now the magnitude of the electrical force on each? When the shperes are brought in contact with each other, the charges will be free to move throughout the two spheres (they are both conducting). Both spheres have the same radius, so geometry will not be an issue. The total charge q 1 + q 2 will evenly distribute itself, so half will go to each sphere. Each sphere has a charge 2 C 8 C 3 C q µ +−+ =
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## This homework help was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Spring '08 term at Iowa State.

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webct11 - 4 corners 1. Three charges Q1, Q2 and Q3 are...

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