A +12 nC charge is located at the origin

In summary, the conversation discussed the electric fields at different positions due to a +12 nC charge located at the origin. The electric field vectors at (x,y) = (5.0 cm, 0 cm), (-5.0 cm, 5.0 cm), and (-5.0 cm, -5.0 cm) were requested in component form. The answers for the second and third positions are (-1.53*10^4 i + 1.53*10^4 j) N/C and (-1.53*10^4 i - 1.53*10^4 j) N/C, respectively. These values were found using the pythagorean theorem to determine the distance from the
  • #1
rushton_19
7
0
A +12 nC charge is located at the origin.

What are the electric fields at the positions (x,y) = (5.0 cm, 0 cm), (-5.0 cm, 5.0 cm), (-5.0 cm, -5.0 cm)? Write each electric field vector in component form.

I got the answer for the first one, but I can't figure out how to get the answers for the second and third ones. The answers are suppose to be (-1.53*10^4 i + 1.53*10^4 j) N/C and (-1.53*10^4 i - 1.53*10^4 j) N/C, respectively.

Thank you!
 
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  • #2
It's just the same as the first one, except now instead of r=5cm, you have to use the pythagorean theorem to find r.
 
  • #3
I've tried that, but it gives me an answer of 2.16*10^4 N/C , instead of the answer of 1.53*10^4 N/C, and I can't figure out why.
 

What is the electric field at point P located at (3,4)?

The electric field is a vector quantity that describes the magnitude and direction of the force experienced by a unit positive charge at a given point. To calculate the electric field at point P, we can use the formula E = kQ/r^2, where k is the Coulomb's constant, Q is the charge at the origin (+12 nC in this case), and r is the distance from the origin to point P. Plugging in the values, we get E = (9 x 10^9 Nm^2/C^2)(12 x 10^-9 C)/(5^2) = 4.32 x 10^5 N/C, with a direction towards the origin.

What is the potential energy of a test charge of +5 nC placed at point P?

The potential energy is a measure of the work required to bring a test charge from infinity to a given position in the electric field. To calculate the potential energy at point P, we can use the formula U = kQq/r, where k is the Coulomb's constant, Q is the charge at the origin (+12 nC in this case), q is the test charge (+5 nC), and r is the distance from the origin to point P. Plugging in the values, we get U = (9 x 10^9 Nm^2/C^2)(12 x 10^-9 C)(5 x 10^-9 C)/5 = 5.4 x 10^-4 J.

What is the force experienced by a -8 nC charge placed at point P?

The force experienced by a charge at a given point in an electric field is equal to the product of the charge and the electric field at that point. In this case, the force experienced by a -8 nC charge placed at point P is F = (-8 x 10^-9 C)(4.32 x 10^5 N/C) = -3.456 N, directed away from the origin.

What is the electric potential at point P?

The electric potential is a scalar quantity that describes the potential energy per unit charge at a given point in an electric field. It is calculated using the formula V = kQ/r, where k is the Coulomb's constant, Q is the charge at the origin (+12 nC in this case), and r is the distance from the origin to point P. Plugging in the values, we get V = (9 x 10^9 Nm^2/C^2)(12 x 10^-9 C)/5 = 2.16 x 10^5 V.

What is the direction of the electric field at point P?

As mentioned earlier, the electric field is a vector quantity and its direction is determined by the direction of the force experienced by a positive test charge placed at a given point. In this case, the electric field at point P is directed towards the origin, as calculated in the first question. Therefore, the direction of the electric field at point P is towards the origin.

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