Charges q_1 = +1.70 nC, q_2, = +2.90 nC, and q_3 = -3.25 nC are located on three

Question

Charges q_1 = +1.70 nC, q_2, = +2.90 nC, and q_3 = -3.25 nC are located on three corners of a square with sides d = 0.0135 m as shown in the figure. Determine the magnitude and direction of the net electric force acting on charge q_2. Read the problem carefully at least once. Be sure to notice the quantities that are known and those quantities that must be found. The known quantities are the values and locations of each charge. The unknown quantities to be determined are the magnitude and direction of the electric force on q_2. Apply Coulomb's law and the electric field expression, as required. The magnitude of electric force F, /, between any two charges q_a and q_b is given by Coulomb's law. F_ab = k_e |q_a||q_b|/r_ab^2 where k_c. = 8.99 times 10^9 N middot m^2/C^2 is the Coulomb constant and r_ab is the separation distance between the charges. This force is attractive if the two charges are of opposite signs and repulsive if the charges are of the same sign. The unknown quantity to be determined is the magnitude F_2 and the direction of the electric force acting on q_2. This force F_2 is the sum of the electric forces from q_1 and q_3 acting on q_2 F_2 = F_12 + F_32 The magnitudes F_12 and F_32 will be determined in this part of the solution. The magnitude F_12 is F_12 = k_e |q_1||q_2|/r_12 and the magnitude F_32 is F_32 = K_e |q_3||q_2|/r_j2^2 where q_1 = +1.70 nC = +1.70 times 10^-9 C, q_2 = +2.90 nC = +2.90 times 10^-9 C, and q_3 = -3.25 nC = -3.25 times 10^-9 C. What is the value of the separation distance r_12 (in m) between q_1 and q_2? 0 0.0135 m 0.0191 m 0.0270 m none of the above

Explanation / Answer

Here,

for the force between q1 and q2

F12 = 9 *10^9 * 1.70 *10^-9 * 2.90 *10^-9/(0.0135^2)

F12 = 2.43 *10^-4 N/C

for the force between q2 and q3

F23 = 9 *10^9 * 1.70 *10^-9 * 3.25 *10^-9/(0.0135^2)

F23 = 2.72 *10^-4 N/C

NOw, for the net force acting

net force acting on the charge q2 = sqrt(2.43^2 + 2.72^2) *10^-4 N/C at 180 - arctan(2.43/2.72)

net force acting on the charge q2 = 3.65 *10^-4 N/C at 138.2 degree

the net force acting on the charge q2 is 3.65 *10^-4 N/C at 138.2 degree

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the distance r12 is 0.0135 m

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