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A point charge +q is placed at a distanc...

A point charge `+q` is placed at a distance `d` from an isolated conducting plane. The field at a point `P` on the other side of plane is

A

directed perpendicular to the plane and away from the plane.

B

directed perpendicular to the plane but towards the plane.

C

directed radially away from the point charge

D

directed radially towards the point charge.

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the electric field created by a point charge \( +q \) placed near an isolated conducting plane. Here’s a step-by-step solution: ### Step 1: Understand the Setup We have a point charge \( +q \) located at a distance \( d \) from an isolated conducting plane. The conducting plane will respond to the electric field created by the point charge. **Hint:** Visualize the scenario by drawing the point charge and the conducting plane. ### Step 2: Induced Charges on the Conducting Plane When the point charge \( +q \) is brought near the conducting plane, it induces a charge on the surface of the conductor. The side of the conducting plane closest to the charge will have a negative charge induced on it, while the side farthest from the charge will have a positive charge induced. This is due to the movement of free electrons in the conductor. **Hint:** Remember that conductors can redistribute their charges in response to external electric fields. ### Step 3: Analyze the Electric Field The electric field at a point \( P \) on the other side of the conducting plane (away from the point charge) will be influenced by the induced charges. The electric field due to the induced negative charge on the conducting plane will point towards the plane, while the electric field due to the positive charge \( +q \) will point away from the charge. **Hint:** Consider the superposition principle: the total electric field is the vector sum of the fields due to the point charge and the induced charges. ### Step 4: Determine the Direction of the Electric Field at Point P At point \( P \), the electric field due to the positive charge \( +q \) will be directed away from the charge, while the electric field due to the induced negative charge on the conducting plane will be directed towards the plane. However, since point \( P \) is on the opposite side of the plane, the effect of the induced charges will dominate. **Hint:** Think about how the fields from the positive charge and the induced charge interact at point \( P \). ### Step 5: Conclusion The net electric field at point \( P \) will be directed perpendicular to the conducting plane and away from the plane. Thus, the correct answer is that the electric field at point \( P \) is directed perpendicular to the plane and away from the plane. **Final Answer:** The electric field at point \( P \) is directed perpendicular to the plane and away from the plane.
To solve the problem, we need to analyze the electric field created by a point charge \( +q \) placed near an isolated conducting plane. Here’s a step-by-step solution: ### Step 1: Understand the Setup We have a point charge \( +q \) located at a distance \( d \) from an isolated conducting plane. The conducting plane will respond to the electric field created by the point charge. **Hint:** Visualize the scenario by drawing the point charge and the conducting plane. ### Step 2: Induced Charges on the Conducting Plane ...
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