Question

In the parallel-plate capacitor of Fig. 24.2, suppose the Plates are pulled apart so that the separation d is much larger than the size of the plates. (a) Is it still accurate to say that the electric field between the plates is uniform? Why or why not? (b) In the Situation shown in Fig. 24.2, the potential difference between the Plates is . If the plates are pulled apart as described above, is Vab more or less than this formula would indicate? Explain Your reasoning.(c) With the plates pulled apart as described above,is the capacitance more than, less than, or the same as that given by Eq. (24.2)? Explain your reasoning.

Short answer

No, it isn’t accurate to say that the electric field between the two plates is uniform

If a plate of a charged parallel capacitor are pulled apart than the charge Increased

The plates pulled apart as described above,is the capacitance, is less than the given capacitance.

Step-by-step solution

Parallel plate capacitor

An arrangement of two metal plates connected in parallel separated from each other by some distance. Dielectric medium occupies the gap between the plates.

Step 2:Determine the possibility of electric field between the plates is uniform

As equation 24.9 mention the potential energy stored in a capacitor is given by

Where Q is the magnitude of the charge on each plate, C is the capacitance and V is the potential difference between the plates.

As equation 24.2 mention, the capacitance of the parallel plate capacitor in a vacuum is given by

Where A is the area of each plate and d is the distance between the two plates. Substituting from the previous calculation, then we get

(a) Solution:

It isn’t still accurate to say that the electric field between the two plates is uniform. Because the separation between the two plates is much larger than the size of the plates. So, we can consider each plate as an end of the one platewhileneglecting the separation between them.

Therefore , No, it isn’t accurate to say that the electric field between the two plates is uniform

Step 3:Determine the effect on potential difference If the plates are pulled apart as described

(b) Solution:

As we know when the plates are pulled, then the separation between them will increase. Due to the given equation, the potential between the two plates is directly proportional to the separation between them. Then the potential between the two plates will increase. So, in this case, the potential is greater than the potential given by the formula.

Therefore , the potential between the two plates will increase

effect on capacitance

(c) Solution:

As we know the capacitance of the parallel plates capacitor is inversely proportional to the separation between them. So, in the case of increasing the separation by pulling the plates, the capacitance will decrease. So the capacitance, in this case, is less than the given capacitance.

Therefore , the plates pulled apart as described above,is the capacitance, is less than the given capacitance.

Result

No, it isn’t accurate to say that the electric field between the two plates is uniform. Because separation between the two plates is much larger than the size of the plates. So, consider each plate ascend of one plate with neglecting the separation between them.

(a) If the plates are pulled, separation between them will increase. Then the potential between the two plates will increase. So, in this case, the potential is greater than the potential given by the formula.

The capacitance, in this case, is less than the given capacitance.