Question

A conducting sphere 45 cm in diameter carries an excess of charge, and no other charges are present. You measure the potential of the surface of this sphere and find it to be 14 kV relative to infinity. Find the excess charge on this sphere.

Answer 1

Answer:

The excess charge is $Q = 3.5 *10^{-7} \ C$

Explanation:

From the question we are told that

      The diameter is $d = 45 \ cm = 0.45 \ m$

       The potential of the surface is $V = 14 \ kV = 14 *10^{3} \ V$

     

The radius of the sphere is  

           $r = \frac{d}{2}$

substituting values

          $r = \frac{0.45}{2}$

         $r = 0.225 \ m$

The potential on the surface is mathematically represented as  

          $V = \frac{k * Q }{r }$

Where k is coulomb's constant with value  $k = 9*10^{9} \ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.$

  given from the question that there is no other charge the Q is the excess charge  

Thus  

        $Q = \frac{V* r}{ k}$

substituting values

        $Q = \frac{14 *10^{3} 0.225}{ 9*10^9}$

        $Q = 3.5 *10^{-7} \ C$