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Three equally charged small objects are placed as shown in the figure. The object A exerts an electric force on object B equal to 3.0 x 10-6 N. (i) Calculate the electric force exerted by C on B? (ii) Calculate the net electric force on B.?
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Three equally charged small objects are placed as shown in the figure....
(i) Electric force exerted by C on B:

The electric force exerted by C on B can be calculated using Coulomb's law:

F = k(q1q2)/r^2

where F is the force, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the objects, and r is the distance between them.

Since all three objects are equally charged, we can assume that they have the same charge q. The distance between C and B is 2r, so the force exerted by C on B is:

F(CB) = k(q^2)/(2r)^2 = k(q^2)/16r^2

Using the value of k and q, we get:

F(CB) = (9 x 10^9 Nm^2/C^2)(q^2)/(16r^2) = (9 x 10^9 Nm^2/C^2)(3.0 x 10^-6 C^2)/(16(0.02 m)^2)

F(CB) = 2.11 x 10^-2 N

Therefore, the electric force exerted by C on B is 2.11 x 10^-2 N.

(ii) Net electric force on B:

The net electric force on B is the vector sum of the forces exerted by A and C on B. Since the forces are in opposite directions, we need to subtract the force exerted by C from the force exerted by A:

F(net) = F(AB) - F(CB) = 3.0 x 10^-6 N - 2.11 x 10^-2 N

F(net) = -2.11 x 10^-2 N

The negative sign indicates that the net force is in the opposite direction to the force exerted by C.

Explanation:

The electric force between charged objects depends on the magnitude of the charges and the distance between them. Coulomb's law is used to calculate the electric force between two charged objects. In this question, we have three equally charged objects placed at a certain distance from each other. The force exerted by A on B is given, and we are asked to calculate the force exerted by C on B and the net force on B.

To calculate the force exerted by C on B, we use Coulomb's law and assume that all three objects have the same charge. The distance between C and B is twice the distance between A and B, so the force exerted by C on B is smaller than the force exerted by A on B.

To calculate the net force on B, we need to consider the vector sum of the forces exerted by A and C on B. Since the forces are in opposite directions, we need to subtract them to get the net force. The negative sign indicates that the net force is in the opposite direction to the force exerted by C.

Overall, this question tests the student's understanding of Coulomb's law and vector addition of forces.
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Three equally charged small objects are placed as shown in the figure. The object A exerts an electric force on object B equal to 3.0 x 10-6 N. (i) Calculate the electric force exerted by C on B? (ii) Calculate the net electric force on B.?
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