Particle A of charge 3.15 times 10^-4 C is at the origin, particle B of charge -

Question

Particle A of charge 3.15 times 10^-4 C is at the origin, particle B of charge -5.82 times 10 C^-4 C is at (0, 3.00 m), and particle C of change 1.04 times 10^-4 C is at (0, 3.00 m). We wish to find the net electric force on C what is the x component of the electric force exerted by A on C? What is the y component of the force exerted by A on C? Find the magnitude of the force exerted by B on C. Calculate the x component of the force exerted by B on C Calculate the y component of the force exerted by B on C Sum the two x components from parts (a) and (d) to obtain the resultant x component of the electric force acting on C Similarly, find the y component of the resultant force vector acting on C. Find the magnitude and direction of the resultant electric force acting on C. magnitude N direction degree counterclockwise from the +x-axis

Explanation / Answer

(a) A and C are both positive ... so they repel each other

The force exerted by A on C [F(AC)] is along the y-axis so has no x-component

so x-component of F(AC) = 0 N

(b) y-component of F(AC) = [9 x 10^9 x 3.15 x 10^(-4) x 1.04 x 10^(-4)] / 3.00^2 = 32.76 N

(c) magnitude of F(BC) = [9 x 10^9 x -8.00 x 10^(-4) x 3.00 x 10^(-4)] / (3.00^2 + 4.00^2) = 11.79 N ... [negative just means it's an attractive force]

(d) angle ACB = arctan (4.00 / 3.00) = 52.7°

so angle F(BC) makes with the positive x-axis is 270 + 52.7 = 322.7°

so x-component of F(BC) = -270 sin 322.77° = 208.7N ... [using the picture to get the ratio required]

(e) y-component of F(BC) = -270 cos 322.77° = -171.2 N

(f) x-component of the resultant electric force on C = 0 + 208.7= 208.7 N

(g) y-component of the resultant electric force on C = 472.5 + -171.2 = 301.3 N

(h) magnitude of the resultant electric force on C = [208.7² + 171.2²] = 269.9 N

Direction of the resultant electric force on C = arctan (171.2 / 208.7) = 50.6° right from the y-axis ...

so that is 90 - 50.6 = 39.4° counterclockwise from the +x-axis

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