Five charges are arranged such that they form a \"+\". The central charge has a

Question

Five charges are arranged such that they form a "+". The central charge has a value of -5.0*10-6 C. The top charge has a value of +1.5 *10-6 C and the right charge also has this same value. The left charge has a value of -5.0*10-6 C and so does the bottom charge. The distance from the center out to each of the individual charges is 1.5 cm.

a.What is the magnitude of the total force acting upon the central charge?

b.What is the direction of the force acting upon the central charge? In degrees.

Please explain. Thanks

Explanation / Answer

Coulombs Law: F=kqq/r^2 F_top on middle: k(1.5E-6)(5E-6)/(0.015)^2 directed up because opposite sign F_bott on middle: k(5E-6)(5E-6)/(0.015)^2 directed up because same sign F_left on middle: k(5E-6)(5E-6)/(0.015)^2 directed right because same sign F_right on middle: k(1.5E-6)(5E-6)/(0.015)^2 directed right because opposite sign F_left-right: k(5E-6)/(0.015)^2 * (5E-6+1.5E-6) to the right F_up-down: k(5E-6)/(0.015)^2 * (5E-6+1.5E-6) upward F_tot= sqrt(F_lr^2+F_ud^2) And the direction is given by the trig relation: arctan(F_ud/F_lr) = theta, which will be positive since you're pointing in the first quadrant.

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