Atiny object carrying a charge of +44 μc and a second tiny charged object are initially very far apart. if it takes 21 j of work to bring them to a final configuration in which the +44 μc object i is at x = 1.00 mm, y = 1.00 mm, and the other charged object is at x = 1.00 mm, y = 3.00 mm (cartesian coordinate system), find the magnitude of the charge on the second object. (k = 1/4πε 0 = 8.99 × 109 n · m2/c2)

The magnitude of the second charge is or

Explanation:

The work done in bringing a charged particle from one point to another in the presence of some electric field is equal to the change in the electric potential energy of the charge in moving from one point to another.

The electric potential energy of some charge at a point in the electric field of another charge is given by the product of the amount of charge and electric potential at that point due to the charge .

The electric potential at that point is given by

where is the Coulomb's constant.

Therefore,

Now, We have given two charges and , whose value is to be found.

When the two charges are infinitely dar apart, the electric potential energy of the system is given by

When the coordinates of position of the two charges are

The distance between the two charges is given by

The electric potential energy of the charges in this configuration is given by

The change in the electric potential energy of the system is equal to the work done to bring the system from inifinitely far apart position to given configuration.

Therefore,

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