The four cases above all show a ball with a charge of ?3q at the top right corne

Question

The four cases above all show a ball with a charge of ?3q at the top right corner of a square. Then there is either one, two, or three additional charged balls, each ball located at a different corner of the square. For parts (b) and (c), use q = 3.30 10-6 C, and L = 60.0 cm, as well as k = 9.00 109 N m2/C2. (a) Rank the cases based on the magnitude of the net electrostatic force experienced by the ball of charge ?3q, from largest to smallest. (b) In Case B, calculate the magnitude of the net electrostatic force acting on the ball of charge ?3q. N (c) In Case D, calculate the magnitude of the net electrostatic force acting on the ball of charge ?3q. N

Explanation / Answer

For all cases use the formula F = kqq/d2 for each charge acting on the -3q charge. Don't forget that force is a vector quantity so you will have to combine the appropriate vectors.

For case A...

F = (9 X 109)(3.3 X 10-6)(-9.9 X 10-6)/.62 = -.817 N (or .817 N pulling west toward to +q charge)

For case B...

F + (9 X 109)(-6.6 X 10-6)(-9.9 X 10-6)/.8492 = .816 N pushing away at a 45o angle N of E

For case C the math is already complete for calculating the individual forces, the two force vectors just need to be combined using the pythagorean theorem.

There is a pull to the West of .817 N and a pull to the South of .817 N

Using c2 = a2 + b2 the resultant force is 1.16 N pulling 45o South of West

For case D the math is also already complete for calculating the individual forces, those three force vectors just need to be combined

There is a pull to the west of .817 N, a pull to the south of .817 N and a push of .816 N at a 45o angle N of East. The component vectors of the .816 N force can be found using the sin and cos functions for a right triangle.

.816(sin45) = .577 N push to the east and .816(cos45) = .577 N push to the North

Combine the North and South you get .24 N pull to the South

Combine the East and West you get .24 N pull to the West

Recombine those vectors with the pythagorean theorem c2 = a2 + b2 = .34 N pull 45o South of West

The magnitude rankings are Case C (1.16 N), Case A (.817 N), Case B (.816 N), Case D (.34 N).

The value of the force for case B is .816 N (and use the direction if needed)

The value of the force for case C is 1.16 N (and use the direction if needed)

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