Question

A small charged bead has a mass of 3.6 g. It is held in a uniform electric field E = (200,000 N/C, up). When the bead is released, it accelerates upward with an acceleration of 24 m/s^2. What is the charge on the bead?

Answer 1

Answer:

The charge on the bead is  $q = 6.084 *10^{-7}\ C$

Explanation:

From the question we are told that

     The  mass of the bead is  $m = 3.6 \ g = 0.0036 \ kg$

      The  magnitude of the electric field is  $E = 200,000 \ N/C$

       The  acceleration of the bead is  $a = 24 m/s^2$

Generally,  the  electric force on the bead is  mathematically represented as  

         $F_ e = q E$

Where q is the charge on the bead

   Now the gravitational force opposing the upward movement of the bead is  mathematically represented as

       $F_g = mg$

Generally the net force on the bead is  mathematically represented as

       $F = F_e - F_g = m* a$

=>    $qE - mg = ma$

Now substituting values

       $q * 200000 - 0.0036 *9.8 = 0.0036 * 24$

     $q = 6.084 *10^{-7}\ C$