Potential Energy of Interaction of Point Charges Quiz
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Questions and Answers

In the context of the connected charged spheres, why must the charges on the spheres be equal in equilibrium?

  • To establish a uniform electric field
  • To conserve momentum
  • To ensure conservation of angular momentum
  • To maintain the potential difference (correct)

    • What is the condition for the ratio of the magnitudes of the electric fields at the surfaces of the charges?

  • $E_1 r_1 = E_2 r_2$
  • $E_1 r_2 = E_2 r_1$ (correct)
  • $E_1 r_1^2 = E_2 r_2^2$
  • $E_1 r_2^2 = E_2 r_1^2$

    • What is the formula for calculating the potential difference in an electric field?

  • $V_A - V_B = Ed$
  • $V_B - V_A = Ed$
  • $V_B - V_A = qE$ (correct)
  • $V_A - V_B = qE$

    • What does the uniform electric field magnitude of 325 V/m represent in the given scenario?

    <p>Electric Field Strength</p> Signup and view all the answers

    Which quantity helps in analyzing how much a force applied to an object changes its momentum?

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

    In an elastic collision, what quantity is conserved?

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

    What is the net force exerted by the two 2.00 mC charges on the test charge q at the origin?

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

    In the given array of charges, what is the total energy required to assemble them?

    <p>Depends on the distance between the charges</p> Signup and view all the answers

    For a spherical conductor with a charge of 26.0 mC, what is the electric field at a distance of 20.0 cm from its center?

    <p>Higher than at $r = 10.0$ cm</p> Signup and view all the answers

    What is the electric field at the origin due to the two 2.00 mC charges?

    <p>Depends on the distance from the charges</p> Signup and view all the answers

    At the midpoint of the base of the isosceles triangle with three charges, what would be the electric potential with $q = 7.00 μC$?

    <p>$0$ V</p> Signup and view all the answers

    What is the formula for the potential energy of a system of two charges separated by a distance $r_{12}$?

    <p>$U_{12} = k \frac{q_1 q_2}{r_{12}}$</p> Signup and view all the answers

    In the context of the charges discussed, what does $W$ represent?

    <p>Work done to bring a charge from infinity to a point</p> Signup and view all the answers

    What is the formula for the electric potential $V_P$ at point $P$ due to two charges at positions (0,0) and (0,3.00) m?

    <p>$V_P = 9 \times 10^9 \left(\frac{2}{4} - \frac{6}{5}\right)$</p> Signup and view all the answers

    What is the work required to bring a third charge of 3 mC to point $P$?

    <p>$6.26 \times 10$ Volts</p> Signup and view all the answers

    What is the total potential energy of a system of three charges $q_1$, $q_2$, and $q_3$ separated by distances $r_{13}$ and $r_{23}$?

    <p>$U = k\left(\frac{q_1 q_2}{r_{13}} + \frac{q_1 q_3}{r_{23}}\right)$</p> Signup and view all the answers

    Study Notes

    Potential Energy of Interaction of Point Charges

    • The potential energy of interaction between two point charges q1 and q2 is given by U12 = ke * q1 * q2 / r12, where ke is Coulomb's constant and r12 is the distance between the charges.

    • This potential energy is equal to the work done to bring the two charges from infinity to a distance r12 apart.

    Potential Energy of a System of Multiple Charges

    • The potential energy of a system of multiple charges is given by U = ke * ∑(q1 * q2 / rij), where q1 and q2 are the charges, and rij is the distance between them.

    • The summation is taken over all possible pairs of charges.

    Electric Potential Due to Multiple Charges

    • The electric potential due to multiple charges at a point is given by VP = ke * ∑(qi / ri), where qi is the ith charge, and ri is the distance from the point to the ith charge.

    Example: Electric Potential Due to Two Charges

    • A 2 mC point charge is located at the origin, and a second charge of - 6 mC is located on the y-axis at the position (0.0, 3.00) m.
    • The electric potential due to these charges at point P, whose coordinates are (4.0, 0.0) m, is VP = -6.26 x 10^5 V.

    Work Required to Bring a Charge to a Point

    • The work required to bring a charge to a point is given by W = VP * q, where VP is the electric potential at the point, and q is the charge.

    Example: Two Connected Charged Spheres

    • Two spherical conductors of radii r1 and r2 are separated by a distance much larger than the radius of either sphere.
    • The ratio of the magnitudes of the electric fields at the surfaces of the charges is given by E1 / E2 = r2 / r1.

    Problems

    • Various problems are listed, including calculating electric potential, electric field, and potential energy for different configurations of charges.

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    Description

    Test your understanding of the potential energy of interaction in a system of point charges. Learn how to calculate the work done and the potential energy of two charges separated by a distance. Explore the concepts taught by Prof. Dr. Salah Makhlouf at Assiut University.

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