Two parallel metal plates P and Q are inserted at equal distances… - Vidyadip

Question

Two parallel metal plates P and Q are inserted at equal distances into a plane capacitor as shown in fig. Plates A and B of the capacitor are connected to a battery of e.m.f. V.
a. What are the potentials of the four plates?

a. What are the potentials of the four plates?
b. How will the potentials of plates P and Q and the intensities of the fields in each of the three spaces change after plates P and Q have been connected by a wire?
c..What will happen to the charges on plates A and B, when plates P and Q are connected with a wire?
d. Will there be charges on the plates P and Q after connecting them with a wire?

✓

Answer

a. The plates P and Q divide the space between the plates A and B in three equal parts. Since V = Ed, the potentials of the plates A, P, Q, and B will be respectively V, 2V/3, V/3 and 0.
b. When the plates P and Q are connected with a wire, the space between the plates A and B gets divided into two equal parts. Hence, the potentials of plates A, P, Q, and B will be respectively V, V/2, V/2 and 0.
Since the potential difference between the plates A and P; and between the plates, Q and B have increased from V/3 to V/2, the electric field between these plates will increase. As the potential difference the plates P and Q is zero, the electric field will also be zero.
c. Since the potential difference between the plates A and P and between the plates Q and B have increased, the charge on the plates A and B will increase.
d. Yes, the plate P will have a positive charge and the plate Q will have a negative charge.

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