Electric Potential and Field Diagram - True/False

• John123
In summary: T: The greater of the two electric fields will be greater. 3. The E field at a is zero. - T: Same as 14. The E field at c is zero. - T: Same as 25. a, b, and c all lie on the same equipotential surface. - T: All three points lie on the same "equipotential surface" which is just a fancy way of saying that they are all on the same plane.6. The potential at a is zero. - F: (see above)7. The potential at b is zero. - F: (see above)
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

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

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BvU said:
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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)

John123 said:
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?

John123 said:
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 ?

BvU said:
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!

John123 said:
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.
John123 said:
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.
John123 said:
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.

1. Is electric potential the same as electric field?

No, electric potential and electric field are two different concepts. Electric potential is a measure of the potential energy per unit charge at a specific point in space, while electric field is a measure of the force per unit charge at a specific point in space.

2. Can an electric field exist without an electric potential?

No, an electric field cannot exist without an electric potential. The electric potential creates the electric field, and the strength of the electric field depends on the magnitude of the electric potential.

3. Are electric potential and electric field vectors or scalars?

Both electric potential and electric field are vectors. This means they have both magnitude and direction.

4. Is the electric potential always positive?

No, the electric potential can be both positive and negative. It depends on the location and the source of the electric field. An electric potential is positive if work is done on a positive charge to move it from infinity to that point, while it is negative if work is done by the electric field to move the charge from infinity to that point.

5. Is the strength of an electric field directly proportional to the electric potential?

Yes, the strength of the electric field is directly proportional to the electric potential. The greater the electric potential, the stronger the electric field and vice versa.

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