# Electric field at a point problem

In summary, the electric field at the dot can be calculated by finding the distance from charge A to the point, using the equation E = kq/r^2 and determining the individual contributions from each charge. However, it is important to use the correct signs and perform the calculations symbolically before plugging in numbers. Additionally, there may be a special formula that can be used to find the components, but more information is needed.

## Homework Statement

In the figure above, charge A is -5.00 nC, charge B is 10.0 nC, and charge C is 5.00 nC. If x = 2.10 cm and y = 4.20 cm, what is the electric field at the dot?

E = kq/r^2

## The Attempt at a Solution

r = distance from A to point = sqrt(x^2+y^2)
Ea = kq/r^2 = -20'414.6 N/C
Ec = kq/x^2 = 102'040.8 N/C
Eb = kq/y^2 = 51'020.4 N/C
Eax = -20'414.6cos63.4 = -9'140.8 N/C
Eay = -20'414.6sin63.4 = -18'253.8 N/C
Enetx = Eax-Ec = -111'181.6 N/C
Enety = Eay-Eb = -69'274.2 N/C
Enet = sqrt[(-111'181.6)^2 + (-69'274.2)^2]
theta = tan^-1(Enety/Enetx) = 32 degrees

Final Answer (which was wrong): 1.13x10^5 @ 32 clockwise from horizontal

Can anyone tell me where I went wrong? Supposedly there is a special formula that I am supposed to use to find the components but I have never seen/used it before.

#### Attachments

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Enetx = Eax-Ec
You calculated the individual contributions all on the basis of right and down are positive. So why are you performing a subtraction to find their sum?

Also, please get into the habit of working purely symbolically, not plugging in numbers until the end. It has many advantages, including making your work much easier to follow and verify.

BeyondBelief96

## What is an electric field?

An electric field is a physical quantity that describes the strength and direction of the force that a charged particle experiences at a particular point in space.

## How is electric field at a point calculated?

The electric field at a point is calculated by dividing the force felt by a charged particle at that point by the charge of the particle. This gives the electric field strength in units of Newtons per Coulomb (N/C).

## What factors affect the strength of the electric field at a point?

The strength of the electric field at a point is affected by the magnitude and direction of the charge creating the field, as well as the distance from the point to the source charge.

## How is the direction of the electric field at a point determined?

The direction of the electric field at a point is determined by the direction in which a positive test charge would move if placed at that point. The field lines always point away from positive charges and towards negative charges.

## Can the electric field at a point be negative?

Yes, the electric field at a point can be negative. This indicates that the force on a positive test charge at that point would act in the opposite direction of the field line, towards the source charge.

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