A +4.0 uC charge is placed on the x axis at x= +3.0 m, and a -2.0 uC is located on the y-axis at y= -1.0 m. Point A is on the y axis at y= +4.0 m. Determine the electric potential at point A (relative to zero at the origin).

Answers

Answer 1

Answer:

The potential is  [tex]V_A = 9600 \ V[/tex]

Explanation:

From the question we are told that  

   The  magnitude of the charge is  [tex]q_1 = 4 \mu C = 4*10^{-6} \ C[/tex]

   The position of the charge is  [tex]x = + 3.0 \ m[/tex]

   The magnitude of the second charge is  [tex]q_2 = -2.0 \mu C = -2.0 *10^{-6} \ C[/tex]

   The position is  [tex]y_1 = - 1.0 \ m[/tex]

     The position of point A is  [tex]y_2 = + 4.0 \ m[/tex]  

Generally the electric potential  at A due to the first charge is mathematically represented as

         [tex]V_a = \frac{k * q_1 }{r_1 }[/tex]

Here k is the coulombs constant with value [tex]k = 9*10^{9} \ \ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}[/tex]

        [tex]r_1[/tex]  is the distance between first charge and a which is mathematically represented as

         [tex]r_1 = \sqrt{x^2 + y_2 ^2 }[/tex]

=>      [tex]r_1 = \sqrt{3^2 + 4 ^2 }[/tex]    

=>      [tex]r_1 = 5 \ m[/tex]    

So

           [tex]V_a = \frac{9*10^9 * 4*10^{-6} }{5 }[/tex]

      [tex]V_a = 7200 \ V[/tex]

Generally the electric potential  at A due to the second charge is mathematically represented as

         [tex]V_b = \frac{k * q_2 }{r_2 }[/tex]

Here k is the coulombs constant with value [tex]k = 9*10^{9} \ \ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}[/tex]

        [tex]r_2[/tex]  is the distance between second charge and a which is mathematically represented as

         [tex]r_2 = y_2 - y[/tex]

=>      [tex]r _2 = 4.0 - (-1.0)[/tex]    

=>      [tex]r = 5 \ m[/tex]    

So

           [tex]V_a = \frac{9*10^9 * -2*10^{-6} }{5 }[/tex]

      [tex]V_a = -3600 \ V[/tex]

So the net potential difference at point A  due to the charges is mathematically represented as

       [tex]V_n = V_a + V_b[/tex]

=>     [tex]V_n = 7200 - 3600[/tex]

=>     [tex]V_n = 3600 V[/tex]

Generally the net potential difference at the origin due to both charges is mathematically represented as

     [tex]V_N = V_c + V_d[/tex]

Here  

      [tex]V_c = \frac{k * q_1 }{x}[/tex]

=>   [tex]V_c = \frac{9*10^9 * 4*10^{-6} }{3}[/tex]

=>   [tex]V_c = 12000 V[/tex]

and

              [tex]V_d= \frac{k * q_2 }{y}[/tex]

=>   [tex]V_c = \frac{9*10^9 * -2*10^{-6} }{1}[/tex]

=>   [tex]V_c =- 18000 V[/tex]

Generally the net potential difference at the origin is  

       [tex]V_N = 12000 - 18000[/tex]

=>     [tex]V_N = -6000[/tex]

Generally the potential difference at A relative to zero at the origin is mathematically evaluated as

         [tex]V_A = V_n - V_N[/tex]

=>      [tex]V_A = 3600 - (-6000)[/tex]

=>      [tex]V_A = 9600 \ V[/tex]


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