Electrostatic Potential and Energy
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Electrostatic Potential and Energy

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Questions and Answers

What is the sign of the potential difference $V_P - V_Q$ for the given charges?

  • Positive (correct)
  • Negative
  • Undefined
  • Zero

    • When a small negative charge moves from point Q to point P, what can be said about the potential energy difference?

  • It is impossible to determine.
  • It is positive. (correct)
  • It is negative.
  • It is zero.

    • What describes the work done by the field when moving a small positive charge from point Q to point P?

  • Negative work is done. (correct)
  • Work cannot be defined.
  • No work is done.
  • Positive work is done.

    • What is the sign of the work done by the external agency when moving a small negative charge from point B to point A?

    <p>Positive</p> Signup and view all the answers

    How does the kinetic energy of a small negative charge change when moving from point B to point A?

    <p>It decreases.</p> Signup and view all the answers

    What characterizes an equipotential surface?

    <p>Constant potential value</p> Signup and view all the answers

    What occurs when work is done against the electric field when moving a charge?

    <p>Potential energy increases.</p> Signup and view all the answers

    What is the relationship between the signs of potential differences VB - VA, based on their values?

    <p>VB &gt; VA is positive.</p> Signup and view all the answers

    What is physically significant about electric potential?

    <p>It is the potential difference.</p> Signup and view all the answers

    What does the electrostatic potential (V) at a point indicate?

    <p>The work done in bringing a unit positive charge from infinity to that point.</p> Signup and view all the answers

    When calculating the work done to bring a test charge from infinity to a point, what is essential to keep in mind?

    <p>The work only depends on the initial and final positions.</p> Signup and view all the answers

    In the context of electric potential, what is the role of an external force?

    <p>It must be equal and opposite to the electrostatic force at every point.</p> Signup and view all the answers

    What does one need to calculate the potential at point P due to a positive point charge Q?

    <p>The distance from charge Q to point P.</p> Signup and view all the answers

    When determining work done on a test charge by an electrostatic field, what is the nature of the test charge?

    <p>It should be a unit positive charge.</p> Signup and view all the answers

    What can be said about the work done per unit test charge?

    <p>It is determined by the ratio of work done to the charge brought.</p> Signup and view all the answers

    What is the key consideration when defining potential in an electrostatic field?

    <p>It requires a reference point, often taken as zero potential at infinity.</p> Signup and view all the answers

    What happens to the potential energy when the angle of inclination q is chosen to be $\frac{\pi}{2}$?

    <p>Potential energy is set to zero.</p> Signup and view all the answers

    In the expression for potential energy $U'(\theta)$, what does the term $-pE \cos \theta$ represent?

    <p>Work done in moving the dipole against the electric field.</p> Signup and view all the answers

    How do the forces acting on charges +q and -q compare when q is set to $\frac{\pi}{2}$?

    <p>They are equal and opposite.</p> Signup and view all the answers

    What is the significance of the second term in the expression for $U'(\theta)$?

    <p>It remains constant for a given dipole.</p> Signup and view all the answers

    When calculating the potential difference between positions r1 and r2, what does the displacement '2a cos q' represent?

    <p>The distance moved by the unit positive charge.</p> Signup and view all the answers

    In the expression for potential energy due to an electric dipole, what does the symbol 'p' represent?

    <p>Permanent electric dipole moment.</p> Signup and view all the answers

    What is the relationship between the work done and the potential energy for the dipole?

    <p>Work done against the field is equal to the change in potential energy.</p> Signup and view all the answers

    When a strong electric field is applied, what is the effect on a mole of polarized substance with a permanent electric dipole moment?

    <p>Its dipole moments align in the field direction.</p> Signup and view all the answers

    What occurs to the net electrostatic field in a conductor when two opposing fields cancel each other?

    <p>The net field becomes zero.</p> Signup and view all the answers

    What effect does an external electric field have on the molecules of a dielectric?

    <p>It induces a temporary dipole moment.</p> Signup and view all the answers

    Which of the following statements is true about non-polar molecules in an external electric field?

    <p>Their positive and negative charges are displaced in opposite directions.</p> Signup and view all the answers

    What distinguishes polar molecules from non-polar molecules?

    <p>Polar molecules have separated positive and negative charge centers.</p> Signup and view all the answers

    How does a dielectric respond to an external electric field compared to a conductor?

    <p>It reduces the external field but does not cancel it entirely.</p> Signup and view all the answers

    Which of the following accurately describes ionic molecules like HCl in an electric field?

    <p>They have separated positive and negative charges.</p> Signup and view all the answers

    What is the role of the nature of the dielectric concerning its response to an external field?

    <p>It influences the extent of the induced electric field within the dielectric.</p> Signup and view all the answers

    Which molecules are typical examples of non-polar molecules?

    <p>Oxygen (O2) and hydrogen (H2)</p> Signup and view all the answers

    What is the equivalent capacitance C of a network with three capacitors of 10 mF in series and one capacitor of 10 mF in parallel?

    <p>13.3 mF</p> Signup and view all the answers

    In a series connection of capacitors, which statement about charge is true?

    <p>The charge is the same on each capacitor.</p> Signup and view all the answers

    If a capacitor with capacitance C and voltage V has an energy storage formula, which matches the equation for energy stored?

    <p>$U = \frac{1}{2} CV^2$</p> Signup and view all the answers

    How is the charge on capacitor C4 when connected in parallel with three capacitors in series described?

    <p>It carries a different charge than C1, C2, and C3.</p> Signup and view all the answers

    What happens to the equivalent capacitance when capacitors are combined in series?

    <p>It decreases.</p> Signup and view all the answers

    For capacitors connected in series, how does the voltage across each capacitor relate to the total voltage?

    <p>The total voltage is the sum of the voltages across each capacitor.</p> Signup and view all the answers

    If the voltage supply to a series of capacitors is 500 V and the capacitance is configured as in the example, what is the charge on each of the series capacitors?

    <p>1.7 mC</p> Signup and view all the answers

    Which formula correctly represents the relationship of capacitance in parallel configuration?

    <p>C = C1 + C2 + ... + Cn</p> Signup and view all the answers

    Study Notes

    Electrostatic Potential

    • The potential difference is physically significant, not the potential itself.
    • Potential is zero at infinity.
    • Electrostatic potential at a point is the work done in bringing a unit positive charge from infinity to that point.

    Potential Due to a Point Charge

    • The work done by an external force in bringing a unit positive charge from infinity to a point is equal to the electrostatic potential at that point.

    Equipotential Surfaces

    • An equipotential surface has a constant potential value at all points.

    Potential Energy of a Dipole in an External Field

    • The work done by an external force in rotating a dipole is stored as the potential energy of the system.
    • The potential energy of a dipole is given by U(q) = -pE cos q, where q is the angle between the dipole moment and the electric field.
    • The natural choice for zero potential is when q0 = p/2, which leads to U(q) = -pE cos q.

    Polarization of Dielectrics

    • In a strong electrostatic field, molecular dipole moments align until the net field in the conductor is zero.
    • Dielectrics do not allow free movement of charges, but the external field induces dipole moments, which creates an opposing field that reduces the external field.
    • Non-polar molecules have no permanent dipole moment, while polar molecules have a permanent dipole moment.
    • In an external field, non-polar molecules get polarized due to charge displacement.

    Capacitance

    • The equivalent capacitance for capacitors connected in series is given by 1/C = 1/C1 + 1/C2 + ... + 1/Cn.
    • The equivalent capacitance for capacitors connected in parallel is given by C = C1 + C2 + ... + Cn.

    Energy Stored in a Capacitor

    • A capacitor is a system of two conductors with charge Q and -Q.
    • The energy stored in a capacitor is given by U (Q) = Q^2/2C = 1/2 CV^2 = 1/2 QV, where Q is the charge, C is the capacitance, and V is the potential difference.

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    Electrostatic Potential and Capacitance PDF

    Description

    Test your understanding of electrostatic potential concepts, including the significance of potential differences and the behavior of point charges. Explore equipotential surfaces, potential energy of dipoles in external fields, and the effects of dielectrics. This quiz will challenge your knowledge and application of fundamental electrostatic principles.

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