lMaterials Section 185 12.5 points CJ10 18&P018; My Notes O Ask Your Teache A ch

Question

lMaterials Section 185 12.5 points CJ10 18&P018; My Notes O Ask Your Teache A charge of -2.8 IC is fioxced at the center of a compass. Two additional charges are fixed on the circle of the compass, which has a radius of 0.098 m. The charges on the circle are -3.6 JC at the position due north and +4.55 HIC at the position due east. What are the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east. direction magnitude Additional Materials section 18.5

Explanation / Answer

Coulomb's law, force of attraction/repulsion

F = kQQ/r²

Q and Q are the charges in coulombs

r is separation in meters

k = 8.99e9 Nm²/C²

first pair

F = k(2.8µ)(3.6µ) / (0.098)² = 9.446 N

this is repulsive, so it points S

second pair

F = k(2.91µ)(4.55µ) / (0.098)² = 12.408 N

this is attractive so it points E

combine them

F = sqrt[9.446^2 + 12.408^2] = 15.6 N(ans)

Direction = arctan (9.446/12.408) = 37.28 degrees south of east

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