Electric Potential and Field Diagram - True/False

[John123]

Homework Statement

Four charges are arranged at the corners of a square as shown in the figure. Q1 is at (-L/2,L/2), Q2 is at (L/2,L/2), point a is at the origin and Q1=Q2=-Q3=-Q4. Which of the following statements correctly describe the electric field E and the potential at points a,b and c? Select true or false for each statement.

1. The potential at c is zero.
2. The magnitude of the E field at b is greater than at c.
3. The E field at a is zero.
4. The E field at c is zero.
5. a, b, and c all lie on the same equipotential surface.
6. The potential at a is zero.
7. The potential at b is zero.
https://imgur.com/a/w4EmPKy

Homework Equations

I attempted to use logical reasoning

The Attempt at a Solution

1. The potential at c is zero. - F
2. The magnitude of the E field at b is greater than at c. - T: the b charge is closer to the point charges hence the electric field is greater
3. The E field at a is zero. - T: E field is a vector hence they all cancel within the middle
4. The E field at c is zero. - T: the E field does not cancel on c
5. a, b, and c all lie on the same equipotential surface. - T: Self-explanatory, they all lie on the x axis
6. The potential at a is zero. - F: E potential is a scalar hence it will not cancel to zero
7. The potential at b is zero. - F

Does anyone see which ones I may have gotten incorrect so I can logically see the correct answers?

Thanks

 

[BvU]

Yes, I can see. But I'll only point out which ones if you add an explanation to each of your conclusions.

 

[John123]

View attachment 238417

Yes, I can see. But I'll only point out which ones if you add an explanation to each of your conclusions.

Ok ill try to in-depth my rational a little more. Thanks!
Essentially for the electric potential ones, since I am still struggling with the concept of it, when its within the vicinity of charges, the E potential can never be zero, since it is a scalar. Therefore, for 1 and 7, they are false since under no way can the potential add up to zero?

1. The potential at c is zero. - F: (see above)
2. The magnitude of the E field at b is greater than at c. - T: the b charge is closer to the point charges hence the electric field is greater
3. The E field at a is zero. - T: E field is a vector hence they all cancel within the middle
4. The E field at c is zero. - T: the E field does not cancel on c since it is past all the charges and they are all acting on 1 direction
5. a, b, and c all lie on the same equipotential surface. - T: Self-explanatory, they all lie on the x-axis hence the same equipotential surface
6. The potential at a is zero. - F: E potential is a scalar hence it will not cancel to zero - similar to my original logic
7. The potential at b is zero. - F (see above)

 

[haruspex]

the E potential can never be zero, since it is a scalar.

Scalars can be zero, even negative.
Potentials, whether electric, gravitational, whatever, are always relative to some chosen zero. In some contexts, it is conventional to take the potential at infinity as zero. To answer the questions here you will need to assume that.

For the field questions, draw the direction of the field due to each charge at the given point.
In 4, you say T but provide a reason for saying F.
For 5, why should the x-axis be equipotential?

 

[BvU]

no way can the potential add up to zero?

What sign has the potential if a negative charge is nearby ? e.g. from Q4 at c ?
What sign has the potential if a positive charge is nearby ? e.g. from Q₂ at c ?
What if two equal, but opposite, charges are at equal distances ? e.g. from Q₂ and from Q₄ at c ?

 

[John123]

What sign has the potential if a negative charge is nearby ? e.g. from Q4 at c ?
What sign has the potential if a positive charge is nearby ? e.g. from Q₂ at c ?
What if two equal, but opposite, charges are at equal distances ? e.g. from Q₂ and from Q₄ at c ?

Ahh that makes a lot of sense. Which leads me to say that

1. The potential at c is zero. - T: The negative potential created from the bottom and the potential created from the top will amount to zero.
2. The magnitude of the E field at b is greater than at c. - T: the b charge is closer to the point charges hence the electric field is greater
3. The E field at a is zero. - T: E field is a vector hence they all cancel within the middle
4. The E field at c is zero. - T: the E field does not cancel on c since it is past all the charges and they are all acting on 1 direction
5. a, b, and c all lie on the same equipotential surface. - T: Self-explanatory, they all lie on the same axis which all amounts to a zero potential
6. The potential at a is zero. - T: Potential created from the top charges and the bottom charges amount to zero.
7. The potential at b is zero. - T (see above)

I hope I am on the right direction

Thanks!

 

[haruspex]

1. The potential at c is zero. - T: The negative potential created from the bottom and the potential created from the top will amount to zero.

Yes, but I think you could add a bit of explanation as to why they exactly cancel.

2. The magnitude of the E field at b is greater than at c. - T: the b charge is closer to the point charges hence the electric field is greater

Again, that's a little glib. Yes, the fields due to the individual charges are less in magnitude at c, but the magnitude of the sum is not the sum of the magnitudes.

3. The E field at a is zero. - T: E field is a vector hence they all cancel within the middle

See post #4 re field questions.