Question

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).

Answer 1

The potential is
`V_A = 9600 \ V`

Step-by-step explanation:

From the question we are told that

The magnitude of the charge is
`q_1 = 4 \mu C = 4*10^(-6) \ C`

The position of the charge is
`x = + 3.0 \ m`

The magnitude of the second charge is
`q_2 = -2.0 \mu C = -2.0 *10^(-6) \ C`

The position is
`y_1 = - 1.0 \ m`

The position of point A is
`y_2 = + 4.0 \ m`

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

`V_a = (k * q_1 )/(r_1 )`

Here k is the coulombs constant with value
`k = 9*10^(9) \ \ kg\cdot m^3\cdot s^(-4) \cdot A^(-2)`

`r_1` is the distance between first charge and a which is mathematically represented as

`r_1 = √(x^2 + y_2 ^2 )`

=>
`r_1 = √(3^2 + 4 ^2 )`

=>
`r_1 = 5 \ m`

So

`V_a = (9*10^9 * 4*10^(-6) )/(5 )`

`V_a = 7200 \ V`

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

`V_b = (k * q_2 )/(r_2 )`

Here k is the coulombs constant with value
`k = 9*10^(9) \ \ kg\cdot m^3\cdot s^(-4) \cdot A^(-2)`

`r_2` is the distance between second charge and a which is mathematically represented as

`r_2 = y_2 - y`

=>
`r _2 = 4.0 - (-1.0)`

=>
`r = 5 \ m`

So

`V_a = (9*10^9 * -2*10^(-6) )/(5 )`

`V_a = -3600 \ V`

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

`V_n = V_a + V_b`

=>
`V_n = 7200 - 3600`

=>
`V_n = 3600 V`

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

`V_N = V_c + V_d`

Here

`V_c = (k * q_1 )/(x)`

=>
`V_c = (9*10^9 * 4*10^(-6) )/(3)`

=>
`V_c = 12000 V`

and

`V_d= (k * q_2 )/(y)`

=>
`V_c = (9*10^9 * -2*10^(-6) )/(1)`

=>
`V_c =- 18000 V`

Generally the net potential difference at the origin is

`V_N = 12000 - 18000`

=>
`V_N = -6000`

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

`V_A = V_n - V_N`

=>
`V_A = 3600 - (-6000)`

=>
`V_A = 9600 \ V`