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two point charges of magnitude 4.0 μc and -4.0 μc are situated along the x-axis at x1 = 2.0 m and x2 = -2.0 m, respectively. what is the electric potential at the origin of the xy-coordinate system?

Respuesta :

oladayoademosu

The electric potential at the origin of the xy coordinate system is negative infinity

What is the electric field due to the 4.0 μC charge?

The electric field due to the 4.0 μC charge is E = kq/r² where

  • k = electric constant = 9.0 × 10 Nm²/C²,
  • q = 4.0 μC = 4.0 × 10 C and
  • r = distance of charge from origin = x₁ - 0 = 2.0 m - 0 m = 2.0 m

What is the electric field due to the -4.0 μC charge?

The electric field due to the -4.0 μC charge is E = kq'/r² where

  • k = electric constant = 9.0 × 10 Nm²/C²,
  • q' = -4.0 μC = -4.0 × 10 C and
  • r = distance of charge from origin = 0 - x₂ = 0 - (-2.0 m) = 0 m + 2.0 m = 2.0 m

Since both electric fields are equal in magnitude and directed along the negative x-axis, the net electric field at the origin is

E" = E + E'

= -2E

= -2kq/r²

What is the electric potential at the origin?

So, the electric potential at the origin is V = -∫₂⁰E".dr

= -∫₂⁰-2kq/r².dr

Since E and dr = dx are parallel and r = x, we have

= -∫₂⁰-2kqdxcos0/x²

= 2kq∫₂⁰dx/x²

= 2kq[-1/x]₂⁰

= -2kq[1/x]₂⁰

= -2kq[1/0 - 1/2]

= -2kq[∞ - 1/2]

= -2kq[∞]

= -∞

So, the electric potential at the origin of the xy coordinate system is negative infinity

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