Electrical field of an equialateral triangle

In summary, an equilateral triangle with 3 rods, each with a length of 10cm, is formed with two carrying a charge of +63nC and one carrying a charge of -63nC. The charge is uniformly distributed along each rod. Using the equation E_Rod = KQ / (d*sqrt(d^2 * (L/2)^2)), where K is a constant, Q is the charge, d is the distance, and L is the length of the rod, the magnitude of the electric field at the center of the triangle can be calculated. After correcting for the distance and splitting the forces into horizontal and vertical components, the net electric field is found to be 197976, which is incorrect
  • #1
phy43
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Homework Statement


An equilateral triangle is formed with 3 rods, each with a length of 10cm. Two of them carry a charge of +63nC and 1 carries a charge of -63nC. The charge is uniformly distributed along each rod. What is the magnitude of the electric field at the center of the triangle?


Homework Equations


E_Rod = KQ / (d*sqrt(d^2 * (L/2)^2))


The Attempt at a Solution


Center of triangle is 4.33cm, or .0433m from each rod.

Constant K = 9.0*10^9
Q: Charge
d: Distance
L: Length of rod
E_Rod = KQ / (d*sqrt(d^2 * (L/2)^2))
E_Rod = (9.0*10^9)Q / (.0433sqrt(.0433^2 + .05^2))
Plugging in 63*10^9, 63*10^9, and -63*10^9, I receive:
E_Rod(1,2,3) = 197976,197976,-197976

Adding the three gives me a net E_rod = 197976, which is wrong.
 
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  • #2
draw a picture of the forces involved. Split them up in horizontal and vertical components and add those.
 
  • #3
Thanks.. Figured it out. Also figured out I was calculating the triangle height wrong.
 

Related to Electrical field of an equialateral triangle

What is the electrical field of an equilateral triangle?

The electrical field of an equilateral triangle is a vector field that describes the strength and direction of the electric force at any point around the triangle. It is represented by arrows pointing away from or towards the triangle, with the length of the arrow representing the strength of the field.

How is the electrical field of an equilateral triangle calculated?

The electrical field of an equilateral triangle is calculated by using Coulomb's Law, which states that the magnitude of the electric field is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In the case of an equilateral triangle, this involves taking into account the charges at each vertex and the distances between them.

What factors can affect the electrical field of an equilateral triangle?

The electrical field of an equilateral triangle can be affected by a few different factors, such as the magnitude and distribution of charges on the triangle, the distance between the charges, and the medium in which the triangle is located. The shape and orientation of the triangle can also have an impact on the electric field.

What is the direction of the electrical field at the center of an equilateral triangle?

At the center of an equilateral triangle, the electrical field points towards the center due to the symmetry of the triangle. This is because the electric forces from each of the charges on the triangle cancel out, leaving only the component that points towards the center.

How does the electrical field of an equilateral triangle change as the distance from the triangle increases?

The electrical field of an equilateral triangle decreases as the distance from the triangle increases, following the inverse square law. This means that the field strength decreases rapidly as the distance increases, and eventually becomes negligible at large distances from the triangle.

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