Electrostatics - Finding amount of heat in a circuit

In summary, the problem involves a solid conducting sphere surrounded by a concentric conducting spherical shell. The goal is to find the amount of heat produced when a switch is closed, and the method used is to calculate the potential energy of the system before and after the switch is closed and take the difference. The attempted solution involves finding the potential energy at each stage, which results in an answer of kq2/2a. However, the correct answer is kq2/4a, so the solution may contain an error.
  • #1
Abhishekdas
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Homework Statement


A solid conducting sphere of radius 'a' having a charge q is surrounded by a concentric conducting sphereical shell of inner radius 2a and outer radius 3a (please refer diagram)...
Find the amount of heat produced when switch is closed ...


Homework Equations





The Attempt at a Solution


I proceeded by finding out the Potential energy(electrostatic) of the system initially and finally and their difference is equal to heat lost...Doing all the calculations i get kq2/2a as theanswer but answer is kq2/4a...
So can anyone try and tell me if my answer is correct or not...

I proceeded as below...
part 1.(before switch is closed)

charge distribution is q in the outer surface of smaller sphere, -q on the inner surface of shell and q on the outer surface of shell...PE of system at this stage is 5kq2/6a.

Part 2(after switch is closed)
charge distribution is 0 on the outer surface of smaller sphere and 0 also on the inner surface of shell and q on the outer surface of shell...
PE of system at this stage is kq2/3a

Difference between Pe = heat so answer is kq2/2a...
 

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  • #2


Please can anyone point out if there is any error?
 

Related to Electrostatics - Finding amount of heat in a circuit

What is electrostatics and how does it relate to heat in a circuit?

Electrostatics is the study of stationary electric charges and their interactions. It relates to heat in a circuit because the movement of charges in a circuit can produce heat through resistance.

How do you calculate the amount of heat produced in a circuit?

The amount of heat produced in a circuit can be calculated using the formula Q = I2Rt, where Q is the heat produced, I is the current flowing through the circuit, R is the resistance of the circuit, and t is the time.

What factors affect the amount of heat produced in a circuit?

The amount of heat produced in a circuit is affected by the amount of current flowing through the circuit, the resistance of the circuit, and the duration of the current flow.

How can you reduce the amount of heat produced in a circuit?

The amount of heat produced in a circuit can be reduced by using materials with lower resistance, increasing the size of the wires to decrease resistance, and reducing the duration of current flow.

What are the potential hazards of excess heat in a circuit?

Excess heat in a circuit can damage components and lead to electrical fires. It can also decrease the efficiency and lifespan of the circuit.

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