Two large, parallel conducting plates X and Y, kept close to each other, are given charges $Q_{1}$ and $Q_{2} (Q_{1} > Q_{2})$ . The four surfaces of the plates are A, B, C and D, as shown in figure. Then :

Question

Verified by Toppr

Answer 1

Let charge for surface A $= Q_{1} - q$ , for surface B $= q$ , for surface C $= Q_{2} - q^{'}$ and for surface D $= q^{'}$ .
As the field inside X plate is zero, $\frac{1}{2 A ϵ _{0}} (Q_{1} - q - q - Q_{2} + q^{'} - q^{'}) = 0$
$- 2 q = Q_{2} - Q_{1} \Rightarrow q = \frac{1}{2} (Q_{1} - Q_{2})$
similarly for Y plate, $\frac{1}{2 A ϵ _{0}} (q^{'} - Q_{2} + q^{'} - q - Q_{1} + q) = 0$
or $2 q^{'} = Q_{1} + Q_{2} \Rightarrow q^{'} = \frac{1}{2} (Q_{1} + Q_{2})$
Thus, charge on A is $Q_{1} - q = Q_{1} - \frac{1}{2} (Q_{1} - Q_{2}) = \frac{1}{2} (Q_{1} + Q_{2})$ .
charge on B is $q = \frac{1}{2} (Q_{1} - Q_{2})$
charge on C is $Q_{2} - q^{'} = Q_{2} - \frac{1}{2} (Q_{1} + Q_{2}) = - \frac{1}{2} (Q_{1} - Q_{2})$
Charge on D is $q^{'} = \frac{1}{2} (Q_{1} + Q_{2})$

Answer 2

Let charge for surface A

= Q_{1} - q

, for surface B

= q

, for surface C

= Q_{2} - q^{'}

and for surface D

= q^{'}

.
As the field inside X plate is zero,

\frac{1}{2 A ϵ _{0}} (Q_{1} - q - q - Q_{2} + q^{'} - q^{'}) = 0

- 2 q = Q_{2} - Q_{1} \Rightarrow q = \frac{1}{2} (Q_{1} - Q_{2})

similarly for Y plate,

\frac{1}{2 A ϵ _{0}} (q^{'} - Q_{2} + q^{'} - q - Q_{1} + q) = 0

or

2 q^{'} = Q_{1} + Q_{2} \Rightarrow q^{'} = \frac{1}{2} (Q_{1} + Q_{2})

Thus, charge on A is

Q_{1} - q = Q_{1} - \frac{1}{2} (Q_{1} - Q_{2}) = \frac{1}{2} (Q_{1} + Q_{2})

.
charge on B is

q = \frac{1}{2} (Q_{1} - Q_{2})

charge on C is

Q_{2} - q^{'} = Q_{2} - \frac{1}{2} (Q_{1} + Q_{2}) = - \frac{1}{2} (Q_{1} - Q_{2})

Charge on D is

q^{'} = \frac{1}{2} (Q_{1} + Q_{2})

Two large, parallel conducting plates X and Y, kept close to each other, are given charges $Q_{1}$ and $Q_{2} (Q_{1} > Q_{2})$ . The four surfaces of the plates are A, B, C and D, as shown in figure. Then :

The charge on A is $\frac{1}{2} (Q_{1} + Q_{2})$ .

The charge on B is $\frac{1}{2} (Q_{1} - Q_{2})$ .

The charge on C is - $\frac{1}{2} (Q_{1} - Q_{2})$ .

The charge on D is $\frac{1}{2} (Q_{1} + Q_{2})$

In an isolated parallel-plate capacitor of capacitance C, the four surface have charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ as shown. The potential difference between the plates is :

Two large, parallel conducting plates are placed close to each other. The inner surfaces of the two plates have surface charge densities $+ σ$ and $- σ$ . The other surfaces are without charge. The electric field has a magnitude of :

In an isolated parallel plate capacitor of capacitance C the four surfaces have charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ as shown in the figure. The potential difference between the plates is :

There are four large parallel conducting plates each of Area A, placed parallel to each other. Plates 1, 2, 3, 4 are given charges equal to $q_{1}, q_{2}, q_{3}$ and $q_{4}$ respectively :

X and Y are large,parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure then:

Revise with Concepts

Electric Field and Potential Due to Conductor

Redistribution of Charges Between Parallel Plates

Redistribution of Charges Between Concentric Shells

Two large, parallel conducting plates X and Y, kept close to each other, are given charges Q1​ and Q2​(Q1​>Q2​). The four surfaces of the plates are A, B, C and D, as shown in figure. Then :

The charge on A is 21​(Q1​+Q2​).

The charge on B is 21​(Q1​−Q2​).

The charge on C is -21​(Q1​−Q2​).

The charge on D is 21​(Q1​+Q2​)

In an isolated parallel-plate capacitor of capacitance C, the four surface have charges Q1​,Q2​,Q3​ and Q4​ as shown. The potential difference between the plates is :

Two large, parallel conducting plates are placed close to each other. The inner surfaces of the two plates have surface charge densities +σ and −σ. The other surfaces are without charge. The electric field has a magnitude of :

In an isolated parallel plate capacitor of capacitance C the four surfaces have charges Q1​,Q2​,Q3​ and Q4​ as shown in the figure. The potential difference between the plates is :

There are four large parallel conducting plates each of Area A, placed parallel to each other. Plates 1, 2, 3, 4 are given charges equal to q1​,q2​,q3​ and q4​ respectively :

X and Y are large,parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure then:

Revise with Concepts

Electric Field and Potential Due to Conductor

Redistribution of Charges Between Parallel Plates

Redistribution of Charges Between Concentric Shells

Two large, parallel conducting plates X and Y, kept close to each other, are given charges $Q_{1}$ and $Q_{2} (Q_{1} > Q_{2})$ . The four surfaces of the plates are A, B, C and D, as shown in figure. Then :

The charge on A is $\frac{1}{2} (Q_{1} + Q_{2})$ .

The charge on B is $\frac{1}{2} (Q_{1} - Q_{2})$ .

The charge on C is - $\frac{1}{2} (Q_{1} - Q_{2})$ .

The charge on D is $\frac{1}{2} (Q_{1} + Q_{2})$

In an isolated parallel-plate capacitor of capacitance C, the four surface have charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ as shown. The potential difference between the plates is :

Two large, parallel conducting plates are placed close to each other. The inner surfaces of the two plates have surface charge densities $+ σ$ and $- σ$ . The other surfaces are without charge. The electric field has a magnitude of :

In an isolated parallel plate capacitor of capacitance C the four surfaces have charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ as shown in the figure. The potential difference between the plates is :

There are four large parallel conducting plates each of Area A, placed parallel to each other. Plates 1, 2, 3, 4 are given charges equal to $q_{1}, q_{2}, q_{3}$ and $q_{4}$ respectively :