A particle of mass `5 xx 10^(-6) g` is kept over a large horizantal sheet of charge of denisity `4.0 xx 10^(-6) C m^(-2)` (Figure 30-W5). What charge should be given to this partical so that if released, it does not fall down? How many electrons are to be removed to give this charge? How much mass is decreased due to the removal of these electrons?

Explanation

The electric field in front of the sheet is
` E =sigma/epsion_0=4.0 xx 10^(-6) C m^(-2)`
`= 2.26 xx 10^5 N C^(-1)`.
If a charge q is given to the particle, the electric force qE acts in the uward direction. It will balance the weight of the pqrticle if
`q xx 2.26 xx 10^5 N C^(-1)` `=5 xx 10^(-9) kg xx 908 m s^(-2)`
or `q =4.9 xx 10^(-8)/2.26 xx 10^ 5 C`.
The charge on one electron is `1.6 xx 10^(-19) C`. The number of electrons to be removed
` =2.21 xx 10^(-13( C/1.6 xx 10^(-19) C` `=1.4 xx 10^6`.
Mass decreased due to the removal of these electrons
`= 1.4 xx 10^6 xx 9.1 xx 10^(-31) kg`
`= 1.3 xx 10^(-24) kg`.