A 2.0 mm × 4.0 mm flat carpet acquires a uniformly distributed charge of −10 μC after you and your friends walk across it several times. A 3.0 μg dust particle is suspended in midair just above the center of the carpet.
a. What is the charge on the dust particle?

Explanation:

Let us assume that the carpet is like a large sheet of charge for the dust particle.

Hence, the electric field is as follows.

                E =

Now, the value of will be as follows.

                         =

Now, for the dust particle

                = 0

                          qE = mg

Now, putting the given values into the above formula and calculate the charge as follows.

                qE = mg

           q =

Thus, we can conclude that charge on the dust particle is .

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