Particle A of charge 3.50 x 10-4 C is at the origin, particle B of charge -6.10x

Question

Particle A of charge 3.50 x 10-4 C is at the origin, particle B of charge -6.10x 104 C is at (4.32 m, 0) and particle C of charge 1.30 x 104 C is at (o, 3.34 m) (a) What is the x-component of the electric force exerted by A on C? (b) What is the y-component of the force exerted by A on C? (c) Find the magnitude of the force exerted by B on C. IN (d) Calculate the x-component of the force exerted by B on C. (e) Calculate the y-component of the force exerted by B on C. IN (f) Sum the two x-components to obtain the resultant x-component of the electric force acting on C. (9) Repeat part (f) for the y-component. (h) Find the magnitude and direction of the resultant electric force acting on C magnitude direction counterclockwise from the +x-axis

Explanation / Answer

Distance between A and C is 3.34 m

Distance between B and C is sqrt(4.32^2 + 3.34^2) = 5.46 m

Formula for force = kq1q2/r^2

a) Zero.

A and C are both positive. So they repel each other

The force exerted by A on C is along the y-axis so has no x-component

so x-component of FAC = 0 N

b) y component of the electric force exerted by A on C

= 9*10^9*3.5*10^-4*1.3*10^-4/3.34^2

= 36.70 N

c) The magnitude of the force exerted by B on C.

FBC = 9*10^9*-6.1*10^-4*1.3*10^-4/5.46^2

= -23.94 N [ negative just means it's an attractive force]

d) Angle of BC with the x axis 180 – theta and

tan theta = 3.34/4.32

theta = arctan(3.34/4.32) = 37.71 degreee

so angle FBC makes with the positive x-axis is 270 + 37.71 = 307.71 degree

the x component of the force exerted by B on C. is

-23.94 sin 307.71 degree = -18.94 N minus shows that it is toward left

e). the y component of the force exerted by B on C.

= 23.94 cos 307.71 degree = 14.64 N

f) Sum the two x components from part (a) and (d) = the resultant x component of the electric force acting along x -axis is -18.94 N

g) Sum the two y components from part (a) and (d) = the resultant y component of the electric force acting along y -axis is 36.70 + 14.64 = 51.34 N

h) Resultant of -18.94 and 51.34 is

sqrt((-18.94)^2 + (51.34)^2) = 54.72 N

Direction of the resultant electric force on C = arctan (-18.94 / 51.34) = - 20.25 degree

right from the y-axis

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