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In question 15, if the conducting spheri...

In question 15, if the conducting spherical shell is not earthed but is neutral, then the force on `q_2` is

A

zero

B

`(q_1q_2)/(4piepsilon_0r^2)`

C

`(q_1q_2)/(4piepsilon_0(r-R)^2)`

D

none of these

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the situation involving a neutral conducting spherical shell and a point charge \( q_2 \) placed outside the shell. Here is a step-by-step solution: ### Step 1: Understand the Configuration We have a neutral conducting spherical shell and a point charge \( q_2 \) located outside the shell. Since the shell is neutral and not earthed, it will not have any net charge. **Hint:** Remember that a neutral conducting shell will have induced charges when an external charge is present. ### Step 2: Induced Charges on the Shell When the point charge \( q_2 \) is placed outside the neutral conducting shell, it will induce charges on the inner surface of the shell. The inner surface will have a charge of \(-q_2\) (negative charge) due to the presence of \( q_2 \). Consequently, the outer surface of the shell will have a charge of \( +q_2 \) to maintain the neutrality of the shell. **Hint:** The total charge on a conductor must remain constant; thus, induced charges will adjust accordingly. ### Step 3: Analyze the Forces Acting on \( q_2 \) The force on \( q_2 \) is due to the electric field created by the induced charge on the outer surface of the shell. Since the shell is neutral and the charge distribution is symmetric, the electric field inside the conductor (including the cavity) is zero. **Hint:** Use Gauss's law to understand that the electric field inside a conductor in electrostatic equilibrium is zero. ### Step 4: Calculate the Force on \( q_2 \) The force \( F \) on \( q_2 \) due to the charge on the outer surface can be calculated using Coulomb's law. The effective charge acting on \( q_2 \) is the total charge on the outer surface of the shell, which is \( +q_2 \). The formula for the force is given by: \[ F = k \frac{|q_2| \cdot |q_1|}{r^2} \] where \( k \) is Coulomb's constant, \( q_1 \) is the charge on the outer surface, and \( r \) is the distance from the center of the shell to the charge \( q_2 \). **Hint:** Remember that the distance \( r \) is the distance from the center of the shell to the point charge \( q_2 \). ### Step 5: Conclusion Since the charge on the outer surface of the shell is \( +q_2 \), the force on \( q_2 \) due to the shell will be repulsive. Therefore, the force on \( q_2 \) is directed away from the shell. **Final Answer:** The force on \( q_2 \) is given by: \[ F = k \frac{q_2^2}{r^2} \] where the direction of the force is away from the shell.
To solve the problem, we need to analyze the situation involving a neutral conducting spherical shell and a point charge \( q_2 \) placed outside the shell. Here is a step-by-step solution: ### Step 1: Understand the Configuration We have a neutral conducting spherical shell and a point charge \( q_2 \) located outside the shell. Since the shell is neutral and not earthed, it will not have any net charge. **Hint:** Remember that a neutral conducting shell will have induced charges when an external charge is present. ### Step 2: Induced Charges on the Shell ...
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