A 2.0 m × 4.0 m flat carpet acquires a uniformly distributed charge of −10 μC after you and your friends walk across it several times. A 5.0 μg dust particle is suspended in midair just above the center of the carpet. Required:
What is the charge on the dust particle?

The  charge on the dust particle is  

Explanation:

From the question we are told that

    The length is  

    The width is  

   The charge is  

    The mass suspended in mid-air is

Generally the electric field on the carpet is mathematically represented as

Where is the permittivity of free space with value

substituting values

Generally the electric force keeping the dust particle on the air  equal to the force of gravity acting on the particles

=>    

=>      

=>      

=>