# HELP A question on electricity (electric field and electric potential)

HELP!!!A question on electricity (electric field and electric potential)

## Homework Statement

Three point charges are located at the corners of an equilateral triangle as shown.
http://s5.tinypic.com/2hdvalh.jpg
a) Find the magnitude and direction of the electric field at P
b) Find the magnitude and direction of the electric field at P(The potential at infinity is zero)
c) What is the electric potential energy of a particle with charge 4 µC placed at P?
d) If the mass of the particle is 7.0*10^-11kg, what minimum velocity muse it be given so that it can escape to infinity?

## The Attempt at a Solution

a)E=KQ/r^2
Etotal=(9*10^9x1*10^-6)/0.3^2+(9*10^9x2*10^-6)/0.3^2+(9*10^9x-2.5*10^-6)/0.52^2=216549.06 point up because the top point has the strongest charge (I am not sure whether I got the direction right or not)
b)V=KQ/r
Vtotal=(9*10^9x1*10^-6)/0.3+(9*10^9x2*10^-6)/0.3+(9*10^9x-2.5*10^-6)/0.52=46678.85
c)V=KQ1Q2/r
Vtotal=(9*10^9x1*10^-6x4*10^-6)/0.3+(9*10^9x2*10^-6x4*10^-6)/0.3+(9*10^9x-2.5*10^-6x4*10^-6)/0.52=0.187
d)V=sqrt(2kQ/mr)
m=mass
Vtotal=sqrt((9*10^9x1*10^-6)/(7*10^-11x0.3))+sqrt((9*10^9x2*10^-6)/(7*10^-11x0.3))-sqrt((9*10^9x2.5*10^-6)/(7*10^-11x0.3))=35500654.39
For part d I don't really know how to solve for velocity after I got the voltage

Even though I got the answer for all of them, but I don't think it is the right way to approach the problem, because the answers are either too big or too small

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LowlyPion
Homework Helper

E-Field is a vector field. Direction matters.

You can't just add the x,y scalars all together.

E-Field is a vector field. Direction matters.

You can't just add the x,y scalars all together.

Part a
Etotal=((9*10^9x1*10^-6)/0.3^2)i+((9*10^9x2*10^-6)/0.3^2)i+((9*10^9x-2.5*10^-6)/0.52^2)j=300000i-83210.1j
Sorry, but I am still not sure which direction is the P pointing to, since j>i so i assume that it is pointing upward.

Also, is there any mistake for the other three parts?

LowlyPion
Homework Helper

Part a
Etotal=((9*10^9x1*10^-6)/0.3^2)i+((9*10^9x2*10^-6)/0.3^2)i+((9*10^9x-2.5*10^-6)/0.52^2)j=300000i-83210.1j
Sorry, but I am still not sure which direction is the P pointing to, since j>i so i assume that it is pointing upward.

Also, is there any mistake for the other three parts?

That's better, but there is a mistake in the net component along the i direction. There is a 1μ C in one direction and a 2μ C charge creating an opposing E-field.

The direction is determined by the tan-1 of the j/i

That's better, but there is a mistake in the net component along the i direction. There is a 1μ C in one direction and a 2μ C charge creating an opposing E-field.

Point with 2μC has the positive direction along x-axis, point with 1μC has negative direction along x-axis
therefore, (9*10^9x2*10^-6/0.3^2)-(9*10^9x1*10^-6/0.3^2)=99888.89i

therefore, the answer for part a is 99888.89i-83210.1j since i>j and point with 2μC is greater than point with 1μC, the direction of P should be pointing to the point with 2μC (right)

LowlyPion
Homework Helper

The charge on the right is positive.

The E-field from a positive charge is outward.

The E-field at p will be -i directed. (To the left.)

In the j direction the charge is negative, hence inward, meaning j is upward directed.

The angle is as I have suggested previously.

The charge on the right is positive.

The E-field from a positive charge is outward.

The E-field at p will be -i directed. (To the left.)

In the j direction the charge is negative, hence inward, meaning j is upward directed.

The angle is as I have suggested previously.

Oops, I forgot that the electric field is always moving to the direction of the negative charge...

I am wondering did I do the rest parts (part b, c and d)correctly?
From the answer I got from part a I am pretty sure that I did part b and c correctly, but can you help me with part d? thank you

LowlyPion
Homework Helper

Oops, I forgot that the electric field is always moving to the direction of the negative charge...

I am wondering did I do the rest parts (part b, c and d)correctly?
From the answer I got from part a I am pretty sure that I did part b and c correctly, but can you help me with part d? thank you

What angle is a) pointing?

What angle is a) pointing?

Since the electric field is moving toward the negative charge, then it moves toward both points with 1 $$\mu$$C and -2.5
tan$$\theta$$=opp/adj=100000/83210.1
tan-1(100000/83210.1)=50.2

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did i get the angle in part a) as well as the answers in other parts right?
Sorry for keep asking you whether I got the answer right for other parts...However, it is the only part I got stuck...and I want to get it done as soon as possible...hope you can forgive my rudeness

LowlyPion
Homework Helper

Since the electric field is moving toward the negative charge, then it moves toward both points with 1 $$\mu$$C and -2.5
tan$$\theta$$=opp/adj=100000/83210.1
tan-1(100000/83210.1)=50.2

That would be +50.2° with respect to the -x axis?

d) is the potential energy from c) converted to ½mv²