The charges shown here are fixed in place at the locations shown, Q_1 is +6 muC,

Question

The charges shown here are fixed in place at the locations shown, Q_1 is +6 muC, Q_2 is +4 muC, and Q_3 is -2 muC (a) Complete the free body diagram for the charge Q_1 at the origin. (1) draw an arrow representing the force exerted by Q_2 on Q_1 and label it F_21, (2) draw another arrow representing the force exerted by Q_3 on Q_1 and label it F_31. finally, draw an arrow representing the net (or resultant) force on Q_1 and label it F Make sure the directions and relative lengths of your arrows are correct (b) Find the magnitudes of the forces F_21 and F_31 F_21 = ____ F_31 = ____ (c) Find the magnitude and direction of the net force F_R. Express the direction as an angle relative to one of the coordinate axes.

Explanation / Answer

Given that

charge q1=6*10^-6 C

charge q2=4*10^-6 C

charge q3=-2*10^-6 C

distance r1=10 cm

distance r2=20 cm

now we find the net force of attraction

the force of attraction betwen charge Q1 and Q2=>F12=kq1q2/r2^2=9*10^9*6*4*10^-12/0.2^2=5.4 N

the force of attraction between charge q1 and q3=>F13=9*10^9*6*-2*10^-12/0.1^2=-10.8 N

the net force of attraction Fnet=-10.8i+5.4j

magnitude of the net force Fnet=[10.8^2+5.4^2]^1/2=12.1 N

direction of the net force =>angle=tan^-1(-5.4/10.8)=153.4 degree

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