Coulomb's Law Grade 12 Question -- Net Electric Field affecting a Charge

[David John]

Homework Statement

Examine the charge distribution shown.
b) What is the net electric field acting on charge 1?

Homework Equations

I used the equation E= (kq1/r^2) + (kq2/r^2)

The Attempt at a Solution

I subbed 9.0 x 10^9 in for k, 3.0 x 10^-5 for both q1 and q2, and 2m for r.
My final answer was 135000N/C
Just want to check if my answer is right or if I'm messing something up. Thanks

 

[BvU]

Just want to check if my answer is right

You can do that yourself.

My final answer was 135000N/C

Not even close. And your relevant equation misses a very important feature...

 

[David John]

You can do that yourself.
Not even close. And your relevant equation misses a very important feature...

Can you let me know what I did wrong?

 

[razidan]

a very important detail is that the electric field is a vector field. you have to solve this by components, and use the Pythagorean theorem to find the magnitude and direction of the field.

 

[David John]

a very important detail is that the electric field is a vector field. you have to solve this by components, and use the Pythagorean theorem to find the magnitude and direction of the field.

I'm sorry but I am really lost. So do I use pythagorean theorem to find the r value, then sub it into my equation. And after that, state the direction using theta?

 

[razidan]

I'm sorry but I am really lost. So do I use pythagorean theorem to find the r value, then sub it into my equation. And after that, state the direction using theta?

The forces acting on q1 are due to the fields emanating from q2 and q3 separately! thanks to superposition, the net force is just the (vector) sum of the two.
lucky for you, the question is set up so that the fields at q1 are orthogonal to each other.
so calculate each one separately, and the use the pythagorean theorem to find the magnitude and direction.

 

[David John]

The forces acting on q1 are due to the fields emanating from q2 and q3 separately! thanks to superposition, the net force is just the (vector) sum of the two.
lucky for you, the question is set up so that the fields at q1 are orthogonal to each other.
so calculate each one separately, and the use the pythagorean theorem to find the magnitude and direction.

Not sure if this is what you mean but I used E=kq/r^2 to find the magnitude of q2 and q3. Then I used pythagorean theorem with the two magnitudes I found (both were 16875. So the magnitude of q1 was 23864.9. Is this what you meant or am I still messing this up?

 

[ehild]

Not sure if this is what you mean but I used E=kq/r^2 to find the magnitude of q2 and q3. Then I used pythagorean theorem with the two magnitudes I found (both were 16875. So the magnitude of q1 was 23864.9. Is this what you meant or am I still messing this up?

The charges q2 and q3 are given, you have to find the electric forces due to q2 and q3. How do you calculate them? In what units?

 

[David John]

The charges q2 and q3 are given, you have to find the electric forces due to q2 and q3. How do you calculate them? In what units?
View attachment 221473

In my textbook, a similar example is given and the equation Enet = (kq1/r1^2) + (kq2/r2^2) was used. That's why I

The charges q2 and q3 are given, you have to find the electric forces due to q2 and q3. How do you calculate them? In what units?
View attachment 221473

I'm not sure what formula to use. I think the final units will be in C or N/C

 

[ehild]

In my textbook, a similar example is given and the equation Enet = (kq1/r1^2) + (kq2/r2^2) was used. That's why II'm not sure what formula to use. I think the final units will be in C or N/C

The equation for Enet is not correct. The electric fields add up as vectors!
N/C is unit of electric field strength, but C is the unit of charge. They are not the same!

 

[razidan]

In my textbook, a similar example is given and the equation Enet = (kq1/r1^2) + (kq2/r2^2) was used. That's why II'm not sure what formula to use. I think the final units will be in C or N/C

Units are very important! if i ask you how far away are you, and you answer "3 oranges"... that doesn't really make sense, does it?
you have to know what units you are looking for. if they ask you what the force is on the particle, your answer has to have units of force (such as N or dyne, etc).

now, about the numerical values that you got - they are waaaay to big. look at the value of the charges, on the order of 10^-5. that's 0.00001. very small.
So try again, try inputting the right constants into your calculator and see what you get
(BTW, using the wrong numbers that you got, you did go through the right procedure to find the magnitude, except the answer is wrong).

 

[David John]

Units are very important! if i ask you how far away are you, and you answer "3 oranges"... that doesn't really make sense, does it?
you have to know what units you are looking for. if they ask you what the force is on the particle, your answer has to have units of force (such as N or dyne, etc).

now, about the numerical values that you got - they are waaaay to big. look at the value of the charges, on the order of 10^-5. that's 0.00001. very small.
So try again, try inputting the right constants into your calculator and see what you get
(BTW, using the wrong numbers that you got, you did go through the right procedure to find the magnitude, except the answer is wrong).

I'm not sure if this is right either but I tried using a different formula, here are my steps:
Fnet = kq1q2/r2
= (9.0 x 10^9)(2.0 x 10^-5)(3.0 x 10^-5) / (2)^2
= 1.35 N
This is the magnitude between q1 and q3 as well, so I then used pythagorean theorem to find the final magnitude which I found to be 1.91 N. Am I getting closer or is this still wrong?

 

[razidan]

I'm not sure if this is right either but I tried using a different formula, here are my steps:
Fnet = kq1q2/r2
= (9.0 x 10^9)(2.0 x 10^-5)(3.0 x 10^-5) / (2)^2
= 1.35 N
This is the magnitude between q1 and q3 as well, so I then used pythagorean theorem to find the final magnitude which I found to be 1.91 N. Am I getting closer or is this still wrong?

this is right. what about the direction?
It is helpful to sketch the problem and draw arrows, representing the forces due to each charge.

 

[David John]

Okay, I decided to just write it all out on paper so I can show what I'm doing. Is this correct?

 

[razidan]

Okay, I decided to just write it all out on paper so I can show what I'm doing. Is this correct?

This is correct.

 

[David John]

This is correct.

I was wondering if the vector arrows I drew are in the right direction? Should the vectors be acting on q1 instead?

 

[David John]

I was wondering if the vector arrows I drew are in the right direction? Should the vectors be acting on q1 instead?

Also, for the first part, it asks for the net force acting on charge 1. Isn't what I sent a photo of answer the first part of the question. I saw on another website that to find the net electric field, I have to take the net force and divide it by q1 to get a final answer in N/C. Is this right?

 

[razidan]

I was wondering if the vector arrows I drew are in the right direction? Should the vectors be acting on q1 instead?

They are correct. opposite charges attract, so q1 is feeling an attraction force, being pulled towards q2 and q3, so the arrows representing the force should also be pointed towards q2 and q3.

Also, for the first part, it asks for the net force acting on charge 1. Isn't what I sent a photo of answer the first part of the question. I saw on another website that to find the net electric field, I have to take the net force and divide it by q1 to get a final answer in N/C. Is this right?

The electric force (measured in N) is $\vec{F_{electric}}=q\vec{E}$, where $\vec{E}$ is the electric field, measured in N/C.

 

[lekh2003]

I've done this exact style of question in my studies of physics, only my one involved a scalene triangle which brought some trig into the problem... It really helped me understand the properties of the electric vector field. Confused me quite a lot though.

But I grasped it after drawing vector diagrams for each charge and thinking about the vectors affecting each one.