At which point or points is the electric field zero in figure?

I can not post the picture, but this is what it looks like:

1 2 3 4(4+)5 6(-)7 8 9 10

The (4+) is a proton with 4 charges.
The (-) is an electron with 1 charge.
They are on a number line 1-10.
The proton is between 4&5.
The electron is between 6&7.

I do not know how to start this question, or what to look at.

The answer for Part (a) is 6

For part (b) its 9

where is the force on a + test charge = to zero. Has to be right of the electron.

E=kq/r^2
put the test charge at p, to the right of the electron,

E=k(4q)/(p-4.5)^2-kq/(p-6.5)^2 if E is zero, then

4/(p-4.5)^2=1/(p-6.5)^2

now solve for p

Do you cross multiply the fractions?

I got 3p^2-43p=148.75

Is this right?

yes, "cross multipy). I didn't check your math, looks right. Now write in in satandard quadratic form, and solve for p with the quadratic equation

To determine the points at which the electric field is zero in the given situation, we need to understand the concept of electric field and how it is influenced by charges.

The electric field is a force field created by charges. It exerts a force on other charges that are placed in the field. The direction of the electric field is the direction in which a positive test charge would be pushed or pulled.

In this case, we have a proton (4+) and an electron (-) placed on a number line from 1 to 10. The proton has a charge of +4, while the electron has a charge of -1. The presence of these charges creates an electric field around them.

To find the points where the electric field is zero, we need to consider the directions and magnitudes of the electric fields created by the proton and the electron at various positions on the number line.

Let's analyze each charge individually:

1. The proton (+4) creates an electric field that points away from it.
2. The electron (-1) creates an electric field that points towards it.

Now let's examine the two charges relative to each other:

3. Between positions 4 and 5, the proton is located. The electric field created by the proton points away from it.
4. Between positions 6 and 7, the electron is located. The electric field created by the electron points towards it.

Based on these observations, we can conclude the following:

a) The electric field due to the proton will be in the positive direction (away from the proton) to the right of position 4 and diminishes as you move further away.
b) The electric field due to the electron will be in the negative direction (towards the electron) to the left of position 7 and diminishes as you move further away.

Therefore, the only spot where the electric fields created by the proton and the electron cancel each other out would be between positions 4 and 7, specifically between 5 and 6.

In summary, the electric field is zero between the positions numbered 5 and 6 on the number line.

Please note that this explanation assumes there are no additional charges present and that the charges are stationary.

Ah, the mysterious electric field! Let me shed some humorous light on this. Now, we have a proton lurking between 4 and 5, eagerly trying to attract stuff, and an electron up to its funny business between 6 and 7, trying to repel everything. So, where can we find a moment of peace, or at least a field of zero electric humor?

Well, let's consider the forces at play here. The proton wants to pull things towards it (positive charge), while the electron wants to push them away (negative charge). And since opposites attract and likes repel, we can think of the electric field as a kind of "battlefield" between these two.

In this particular scenario, aha! We found the electric field is zero at point 5, right between the proton and electron. It's like a cease-fire zone, where the two charges balance each other out and take a well-deserved break from their electric bickering. So, grab a chair and enjoy the neutrality!

But wait, there might be a twist! If there are more charges popping up elsewhere on the number line, the electric field might change again. So, keep an eye out for any surprise guests crashing the party and upsetting the peace.

Remember, my friend, when it comes to electric fields, always expect a shocking twist and a humorous turn! Happy neutral hunting!