Parallel plane - electric field and potential

• Deathnote777
In summary, when two parallel plates are connected with a battery and their distance is halved, the charge per unit area increases due to an increase in electric field. The potential difference remains the same as the potential of both plates increases by the same amount. If one plate is earthed and the plates are put closer, the potential difference and number of charges remain the same, but the charge per unit area increases. If the amount of charges on the plates are fixed and one plate is earthed, as the other plate approaches, the potential of the earthed plate will increase and the potential difference will decrease. This is because the potential at a point is a result of the potentials due to all charges, including the other plate.
Deathnote777
parallel plane -- electric field and potential

Homework Statement

Consider 2 plate A and B. They are connected with a battery and their distance is halved. What will happen as a whole ?

The Attempt at a Solution

1. Charge per unit area increase due to increase in electric field.
2. I think the potential difference will not change although there is increase in charges because both A and B 's potential has increased by the same amount. So there will be no change in potential difference.
Am I right ?
I have another question.
1. If one of the plates(connected with battery) is earthed and they are put closer, what would happen ? Will the potential difference, number of charges and electric field change ?
2. If the amount of charges in the plates are fixed. One of the plates,A, is earthed originally. When B is approaching A, the number of charges in A is still constant, but why the potential of B will increase? Isn't it that only the number of charges determines a plate's potential ?Thank you

Last edited:

Deathnote777 said:
1. Charge per unit area increase due to increase in electric field.
2. I think the potential difference will not change although there is increase in charges because both A and B 's potential has increased by the same amount. So there will be no change in potential difference.
Right answer, wrong reason. One has a positive potential and the other negative. If they both increase, keeping a constant difference, then the positive will be more positive and the negative less negative. That fails on grounds of symmetry.
Neither potential changes, yet the charges increase. Do you see how that can be?
1. If one of the plates(connected with battery) is earthed and they are put closer, what would happen ? Will the potential difference, number of charges and electric field change ?
The P.D. is still controlled by the battery, so won't change. As before, the charge will increase.
2. If the amount of charges in the plates are fixed. One of the plates,A, is earthed originally. When B is approaching A, the number of charges in A is still constant, but why the potential of B will increase? Isn't it that only the number of charges determines a plate's potential ?
If A is earthed, its charge will change. Did you mean the charge of B is constant? What do you mean by 'the potential of B will increase'? Do you mean assuming it was positive? What makes you think it would increase? I think the P.D. will decrease.

haruspex said:
Right answer, wrong reason. One has a positive potential and the other negative. If they both increase, keeping a constant difference, then the positive will be more positive and the negative less negative. That fails on grounds of symmetry.
Neither potential changes, yet the charges increase. Do you see how that can be?
I think I am confused here. Why the potential of a plate will not change when the charge density has increased ? Assume there is one plate only. To my knowledge, increase in charge density in the plate will increase the force exerted on a charged object next to the plate. Hence, potential of that plate is increased, isn't it ?

haruspex said:
f A is earthed, its charge will change. Did you mean the charge of B is constant? What do you mean by 'the potential of B will increase'? Do you mean assuming it was positive? What makes you think it would increase? I think the P.D. will decrease.
I assume it is negative

Deathnote777 said:
I think I am confused here. Why the potential of a plate will not change when the charge density has increased ? Assume there is one plate only. To my knowledge, increase in charge density in the plate will increase the force exerted on a charged object next to the plate. Hence, potential of that plate is increased, isn't it ?
Yes, but the potential at a point in space is a result of the potentials due to all charges, including the other plate. As the plates are brought closer, the potential due to the other plate is strengthened. This is how capacitors work - they store a high charge without producing such a large voltage.

Firstly, when the distance between two parallel plates connected to a battery is halved, the electric field between the plates will double. This is because the electric field between two parallel plates is inversely proportional to the distance between them. Therefore, as the distance decreases, the electric field increases.

Secondly, the potential difference between the two plates will also increase. This is because the potential difference is directly proportional to the electric field. As the electric field doubles, the potential difference will also double.

Now, if one of the plates is earthed and they are put closer together, the potential difference between the plates will decrease. This is because the earthed plate will have a constant potential of zero, while the potential of the other plate will decrease due to the increased distance from the earthed plate.

Regarding your second question, the potential of a plate is not solely determined by the number of charges on it. It is also affected by the distance between the plates and the potential of the surrounding environment. In this case, when plate B is approaching plate A, the potential of A remains constant (as it is earthed) but the potential of B increases due to the increased distance from the earthed plate. Therefore, the potential difference between the plates will also increase.

1. What is a parallel plane electric field?

A parallel plane electric field is a type of electric field in which the electric field lines are parallel to each other. This means that the electric field strength is constant at every point between the two parallel planes.

2. How is the electric field strength calculated in a parallel plane electric field?

The electric field strength in a parallel plane electric field can be calculated by dividing the voltage difference between the two planes by the distance between them. This is known as the electric field formula: E = V/d, where E is the electric field strength, V is the voltage difference, and d is the distance between the planes.

3. What is the relationship between electric potential and electric field in a parallel plane electric field?

In a parallel plane electric field, the electric potential is directly proportional to the electric field strength. This means that as the electric field strength increases, the electric potential also increases.

4. How does the electric potential change between the two parallel planes in a parallel plane electric field?

The electric potential between the two parallel planes in a parallel plane electric field is constant. This means that the electric potential does not change as you move between the two planes, as the electric field strength is also constant.

5. What are some real-life applications of parallel plane electric fields?

Parallel plane electric fields have various applications in modern technology, such as in capacitors, parallel plate capacitors, and parallel plate antennas. They are also used in particle accelerators and in medical imaging techniques such as MRI (magnetic resonance imaging).

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