Introduction
This section provides a variety of problems that combine concepts from electric fields, potential, and capacitance. The aim is to strengthen problem-solving skills through application and integration of ideas.
Practice Problems
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Point Charge Field: A +6 μC charge is placed 0.3 m away from a point. Find the electric field at that point.
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Superposition: Two equal charges of +2 μC are located 1 m apart. What is the electric field at the midpoint between them?
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Potential Difference: A charge of +4 μC creates a potential of 1200 V at some point. How far is that point from the charge?
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Capacitance: A capacitor stores 2 × 10⁻³ C of charge when a potential difference of 50 V is applied. What is its capacitance?
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Series Capacitors: Two capacitors, 6 μF and 12 μF, are connected in series across a 24 V battery. Find the equivalent capacitance and the charge on each capacitor.
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Parallel Capacitors: Two capacitors, 10 μF and 20 μF, are connected in parallel across a 12 V battery. Find the total stored energy.
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Work Done: Calculate the work required to move a +1 μC charge from a point at 20 V potential to another point at 80 V potential.
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Electric Field Between Plates: A parallel-plate capacitor with plate separation 2 mm is connected to a 9 V battery. Find the electric field inside the capacitor.
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Dielectrics: A 5 μF capacitor is filled with a dielectric of εr = 3. What is the new capacitance?
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Challenge: A proton is released from rest at the positive plate of a capacitor with a potential difference of 100 V. What is its speed just before it reaches the negative plate? (ignore non-electric forces)
Hints for Selected Problems
- Problem 2: Consider the vector directions of fields; at the midpoint, they point opposite and may cancel or add depending on sign of charges.
- Problem 5: Use the series capacitance formula, then calculate voltage across each capacitor using Q = CV.
- Problem 10: Use energy conservation: qV = ½ mv², with q = e (charge of proton).
Summary
These problems integrate the major concepts of Chapter 4: electric fields, potential, work, and capacitance. They are intended for practice before attempting the chapter test.