Understanding E=F/q: Solving for E at a Specific Point q_p

[Thickmax]

Homework Statement

Calculate Electric field in 2 situations

Relevant Equations

See below

I have the above question and I think I am now understanding it.

We know that

E=F/q

F= K * ((q1*q2)/r^2)

So E = K * ((q1*q2)/r^2*q)But as we need to find the E at point q_p

I'm thinking for solution 1,

E = (K*(q/(r^2*q)))*2 as the forces are equal,

And for solution 2

E = K*(q/(r^2*q) - K*(q/(r^2*q)

Am I barking up the wrong tree?

 

[Delta2]

You mixed up things a bit ...
To put things in some order:
Assume a positive charge $q'$ is in the middle. Then for each of the two cases do:

• Calculate force $F_1$ from $q_1$ to $q'$ both in magnitude and direction
• Calculate force $F_2$ from $q_2$ to $q'$ both in magnitude and direction
• Calculate the electric field $E_1=F_1/q'$ from $q_1$ both in magnitude and direction
• Calculate the electric field $E_2=F_2/q'$ from $q_2$ both in magnitude and direction
• Calculate the total electric field which will be $E=E_1+E_2$ if $E_1,E_2$ have the same direction, or $E=|E_1-E_2|$ if $E_1,E_2$ have opposite directions (the bars stand for the absolute value).

 

[Steve4Physics]

The question refers to a diagram "… shown on the right in the figure above". This is missing - it is not possible to tell if it is important or not.

This is a badly worded question because the diagrams for Situation 1 and Situation 2 show $q_p=0$ (I assume $q_p$ is the charge on the airplane). This means the airplane experiences no electric field even if an electric field is present (assuming we can ignore induced charges).

Presumably you are being asked for the electric field’s magnitude at the position of the the airplane.

For Situation 1, consider the symmetry. Any charge at the mid-point will experience two equal magnitude forces in opposite directions. What does that tell you?

 

[Thickmax]

I got the answers nearly correct, but for the wrong situations :(

for situation 1 answer is 0,

For situation 2, the answer is 2*k*q/r^2

Thanks for your help :)

 

[Thickmax]

So I Know

E=F/q

F = k*q_1q_2/r^2

So k*q_1*q_2/r^2*q

so to rewrite I have put the sum of the 2, making sure q_2 acts at r_1+r_2^2

((k*q_p)/r_1^2)+((k*q_2)/(r_2+r_1)^2)Is this looking correct?

 

[haruspex]

I got the answers nearly correct, but for the wrong situations :(

for situation 1 answer is 0,

For situation 2, the answer is 2*k*q/r^2

Thanks for your help :)

Judging from the likes, @Steve4Physics and @Delta2 interpret the above post as saying you have now seen how to get the right answers. I read it as saying you are still getting them swapped over.
What you are overlooking is that q1 and q2 are on opposite sides, so if they are like charges their fields oppose and if they are opposite charges their fields add. Draw arrows for the field directions.

 

[haruspex]

View attachment 285450

So I Know

E=F/q

F = k*q_1q_2/r^2

So k*q_1*q_2/r^2*q

so to rewrite I have put the sum of the 2, making sure q_2 acts at r_1+r_2^2

((k*q_p)/r_1^2)+((k*q_2)/(r_2+r_1)^2)Is this looking correct?

I'm confused both by the question and your attempt.
What does it mean by the "electric energy experienced" by a body? Does it mean the force, the field, or the potential energy?
In your attempt, you write the expression for the force cloud 2 exerts on cloud 1, but end up with the expression for the field cloud 2 and the plane produce at cloud 1.

 

[Steve4Physics]

View attachment 285450

So I Know

E=F/q

F = k*q_1q_2/r^2

So k*q_1*q_2/r^2*q

so to rewrite I have put the sum of the 2, making sure q_2 acts at r_1+r_2^2

((k*q_p)/r_1^2)+((k*q_2)/(r_2+r_1)^2)Is this looking correct?

No. It is completely wrong and seems to have nothing to do with the question.

I agree with @haruspex that the question is badly written. Can you tell us what course you are on and where the question is from?

If you have 2 point charges, Q1 and Q2, separated by a distance $d$, what is the standard formula for the electrical potential energy stored? If you don't know, refer to your notes and/or textbook. Then post your reply.

Also, note this is really a new question and ideally should be in a separate thread.

 

[Thickmax]

the answer is apparently
k*(q_1*q_p/r_1 + q_1*q_2/(r_1+r_2))

It is a physics course on edx called pre university physics.

Looking at the difference, my answer is no a million miles away, but you make one mistake in physics and it doesn't really matter.

The question started in a new thread, but got moved into this pre-existing thread, but an administrator.

 

[haruspex]

the answer is apparently
k*(q_1*q_p/r_1 + q_1*q_2/(r_1+r_2))

Ok, that shows the question wants the net electric potential energy of the plane.
The EPE of a charge is its charge multiplied by the electric potential at its location.

 

[Steve4Physics]

Looking at the difference, my answer is no a million miles away, but you make one mistake in physics and it doesn't really matter.t

That's not really true. A mistake (in physics or elsewhere) can be small or big. The mistake you made was fundamental, indicating you didn't really undertsand some basic physics.

It's a bit like confusing velocity and acceleration. It may appear to be a small mistake (e.g. units are m/s and m/s²) but the meanings are very different.

You used a formula giving force instead of the formula giving energy. Though the formulae look similar and are related, they mean very different things.

You never answered the question I asked in Post#8. Here is the question, slightly revised, if you would like to answer it:

You have 2 point charges, Q1 and Q2, separated by a distance d.
What is the formula for the force exerted on each charge?
What is the formula for the electrical potential energy stored?
Refer to your notes and/or textbook if required. And post your reply.

If we can't learn from our mistakes, we are doomed to repeat them!

 

[Thickmax]

That's not really true. A mistake (in physics or elsewhere) can be small or big. The mistake you made was fundamental, indicating you didn't really undertsand some basic physics.

It's a bit like confusing velocity and acceleration. It may appear to be a small mistake (e.g. units are m/s and m/s²) but the meanings are very different.

You used a formula giving force instead of the formula giving energy. Though the formulae look similar and are related, they mean very different things.

You never answered the question I asked in Post#8. Here is the question, slightly revised, if you would like to answer it:

You have 2 point charges, Q1 and Q2, separated by a distance d.
What is the formula for the force exerted on each charge?
What is the formula for the electrical potential energy stored?
Refer to your notes and/or textbook if required. And post your reply.

If we can't learn from our mistakes, we are doomed to repeat them!

Yes exactly, but when do you know you've made your mistake if everything you are doing is an assumption made on best case knowledge, you're adding tomatoes to a fruit salad...

Charge exerted on each charge can be found using Columbs law F=K*((Q1*Q1)/d)

Electrical potential energy = Total Energy - Kinetic Energy

 

[haruspex]

Electrical potential energy = Total Energy - Kinetic Energy

That's not useful here because you don't know the total energy (and besides, that could included gravitational PE, elastic PE, ...).
@Steve4Physics was looking for an equation relating electric potential, charge and electric potential energy.

 

[Steve4Physics]

Yes exactly, but when do you know you've made your mistake if everything you are doing is an assumption made on best case knowledge, you're adding tomatoes to a fruit salad...

Charge exerted on each charge can be found using Columbs law F=K*((Q1*Q1)/d)

Electrical potential energy = Total Energy - Kinetic Energy

In fact, to a botanist, tomatoes are fruit - so adding them to a botanist's fruit salad should not be a problem!

You said:
"Charge [you meant 'Force'] exerted on each charge can be found using Columbs law F=K*((Q1*Q1)/d)"
Your mistakes are:
- not squaring the 'd'
- not using lower-case 'k'
- misspelling "Coulomb's"
(Also you don't need all those brackets.)

I would write F = kQ₁Q₂/d²

That sort of mistake can be avoided simply by learning what Coulomb's law is and how it is expressed mathematically. And if you don't remember, then you look it up. Also, attention to detail is important!

The formula for the energy stored by 2 (point) charges looks similar to the above formula for force. But it is not the same. Don't you have notes or a textbook you can refer to?