Electric Fields and Dipoles - Physics Quiz
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Questions and Answers

What does Gauss's theorem relate to the total electric flux and the charge enclosed by a closed surface?

  • The total electric flux is inversely proportional to the total charge enclosed.
  • The total electric flux is equal to the total charge enclosed multiplied by a constant.
  • The total electric flux is proportional to the square of the total charge enclosed.
  • The total electric flux is equal to the total charge enclosed divided by a constant. (correct)

    • In the expression for electric field due to a point charge, which of the following correctly describes the relationship between the electric field E and distance r?

  • E increases linearly with r.
  • E is constant regardless of r.
  • E is inversely proportional to the square of r. (correct)
  • E is directly proportional to r.

    • Which statement correctly describes the cosine angle θ in the calculation of electric flux when the electric field E and surface element ds are parallel?

  • θ varies depending on the surface orientation.
  • θ is always 90 degrees.
  • θ is always 45 degrees.
  • θ is 0 degrees. (correct)

    • What is the result of integrating the small electric flux dΦ over the closed surface in Gauss's theorem?

    <p>The result is the total electric flux Φ linking the surface.</p> Signup and view all the answers

    When calculating the total electric flux through a spherical surface surrounding a charge q, which expression correctly simplifies the calculations?

    <p>Φ simplifies to $ rac{q}{4 ext{π}ε_0}$ without involving r.</p> Signup and view all the answers

    What happens to the sine components when determining the total electric field from both charges?

    <p>They cancel each other out.</p> Signup and view all the answers

    Which of the following expressions represents the total electric field at point p?

    <p>$E = rac{1}{4eta heta_0} rac{2qa}{(r^{2} + a^{2})^{3/2}}$</p> Signup and view all the answers

    What is the relationship between distance r and the variable u in the expression given?

    <p>$r^2 = u^2 + a^2$</p> Signup and view all the answers

    How does the electric field change with respect to the distance r from the dipole?

    <p>It decreases with the cube of r.</p> Signup and view all the answers

    What is the general formula for the electric field due to an electric dipole?

    <p>$ rac{2q imes a}{ (a^2+x^2)^{3/2}} $</p> Signup and view all the answers

    What does the equatorial line represent in relation to an electric dipole?

    <p>A line that separates the dipole into two equal parts, perpendicular to it.</p> Signup and view all the answers

    Which of the following correctly describes the variables involved in electric field calculations for a dipole?

    <p>Electric field ($E$), distance ($a$), charge ($q$), permittivity of free space ($ heta$).</p> Signup and view all the answers

    What is the purpose of the diagram included in the document regarding the electric dipole?

    <p>To show the vectors related to the electric field at a point along the equatorial line.</p> Signup and view all the answers

    In terms of the dipole moment, which equation specifically indicates the perpendicular components of the electric field?

    <p>$ ar{E}_{Eq} = rac{1}{4 hetaeta} rac{2qa ext{cos} heta}{(a^2 + x^2)^{3/2}} $</p> Signup and view all the answers

    What does the linear charge density measure?

    <p>The electrical charge per unit length of the wire</p> Signup and view all the answers

    What is the role of the cylindrical Gaussian surface in the calculations?

    <p>To simplify the electric field distribution calculations</p> Signup and view all the answers

    Which equation is used to calculate the electric flux through the Gaussian surface?

    <p>$Φ = E imes ds$</p> Signup and view all the answers

    How does the symmetry around the wire affect the electric field calculation?

    <p>It ensures that the electric field's magnitude is constant at all points on a cylindrical surface.</p> Signup and view all the answers

    What is the formula for the electric field intensity E at a distance ρ from the wire?

    <p>$E = rac{eta}{2 heta ho}$</p> Signup and view all the answers

    Which constant is crucial in the formula for electric field intensity?

    <p>Permittivity of free space</p> Signup and view all the answers

    What type of wire is analyzed in this electric field calculation?

    <p>Infinitely long straight wire</p> Signup and view all the answers

    What does the variable ρ represent in the electric field intensity formula?

    <p>The distance from the wire</p> Signup and view all the answers

    What is the electric field inside a uniformly charged spherical shell?

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

    How does the electric field outside a uniformly charged spherical shell behave?

    <p>It resembles that of a point charge at the center.</p> Signup and view all the answers

    Which law is applied to determine the electric field due to a uniformly charged spherical shell?

    <p>Gauss's Law</p> Signup and view all the answers

    In the context of the spherical shell, what do the variables R and r represent?

    <p>R is the radius of the shell, and r is the distance from the center to a point.</p> Signup and view all the answers

    What happens to the electric field intensity as you move further away from a uniformly charged spherical shell?

    <p>It behaves like a point charge and decreases with the square of the distance.</p> Signup and view all the answers

    What is the electric field (E) near a uniformly charged plane sheet of conductor with surface charge density σ?

    <p>$ rac{ au}{2eta_0}$</p> Signup and view all the answers

    What is the direction of the electric field created by a uniformly charged plane sheet of conductor?

    Signup and view all the answers

    What is the electric field (E) at a point located on the surface of a charged spherical shell?

    <p>$\frac{q}{4\pi \epsilon_0 R^2}$</p> Signup and view all the answers

    What can be concluded about the electric field (E) at a point inside a charged spherical shell?

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

    Which equation represents Gauss's law applied to a closed surface around a charge?

    <p>$\Phi = \frac{\Sigma q}{\epsilon_0}$</p> Signup and view all the answers

    In the scenario where point p is located at the surface of the spherical shell, what is the expression for electric flux (Φ)?

    <p>$Φ = ES$</p> Signup and view all the answers

    If the radius of the closed surface is equal to R, how is the electric flux related to the charge and the permittivity constant?

    <p>Electric flux is proportional to the charge divided by the permittivity constant.</p> Signup and view all the answers

    What is the formula for the electric field strength E near a uniformly charged plane sheet of conductor?

    <p>$E = rac{ au}{2 heta}$</p> Signup and view all the answers

    In the calculation of electric field near a plane sheet of conductor, what does σ represent?

    <p>Surface charge density</p> Signup and view all the answers

    What happens to the electric field strength as the distance 'x' from the center of the uniformly charged plane sheet increases?

    <p>It remains constant</p> Signup and view all the answers

    Which statement is true regarding the electric field around a uniformly charged plane sheet?

    <p>The electric field is always perpendicular to the sheet</p> Signup and view all the answers

    Which mathematical theorem is applied to derive the relationship between electric field and surface charge density in this context?

    <p>Gauss's theorem</p> Signup and view all the answers

    Study Notes

    Electric Fields and Dipoles

    • Electric field of a dipole calculated at a point on its equatorial line.
    • The magnitude of electric field at a point P on the equatorial line of a dipole is: $E= \frac{1}{4 \pi \epsilon_0} \frac{2qa}{(r^{2} + a^{2})^{3/2}}$, where:
      • $q$ is the magnitude of each charge in the dipole;
      • $2a$ is the separation between the charges;
      • $r$ is the distance from the center of the dipole to point P.

    Gauss's Theorem

    • Gauss's theorem states that the total electric flux through a closed surface is proportional to the total charge enclosed by the surface.
    • Mathematical representation: Φ = Σ q/ε₀
    • Φ represents the electric flux.
    • Σ q represents the total charge enclosed.
    • ε₀ is the permittivity of free space.

    Electric Field of a Charged Wire

    • An infinitely long straight wire with linear charge density λ produces a radial electric field.
    • The electric field intensity (E) at a point P located at a distance ρ from the wire is: $E = \frac{\lambda}{2\pi\epsilon_0\rho}$.
    • Derivation of the formula uses Gauss's law, considering a cylindrical Gaussian surface surrounding the wire.

    Electric Field of a Charged Spherical Shell

    • The electric field due to a uniformly charged spherical shell depends on the location of the point charge relative to the shell:
      • Inside the Shell: The Electric field is zero.
      • Outside the Shell: The electric field is identical to that of a point charge located at the center of the shell with the same total charge.
    • The formula for the electric field outside the shell is: E = q / (4πε0R2), where q is the total charge of the shell and R is the radius.

    Electric Field Near a Plane Sheet of Conductor

    • The electric field near a uniformly charged plane sheet of conductor is uniform and perpendicular to the sheet.
    • The electric field intensity (E) is: $E = \frac{\sigma}{2\epsilon_0}$, where σ is the surface charge density.
    • The derivation uses a cylindrical Gaussian surface that encloses a portion of the sheet.
    • The electric flux through the curved surface of the cylinder is zero.
    • Applying Gauss's theorem leads to the equation: $2 E S = \frac{\sigma A}{\epsilon_0}$ = $\frac{σ(2 \pi r L)}{ε_0}$, where S is the area of each end of the cylinder, A is the area of the sheet enclosed by the cylinder, and L is the length of the cylinder.
    • Solving for E results in the above formula.

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    Description

    Test your understanding of electric fields and dipoles with this quiz. Explore concepts such as the electric field of a dipole, Gauss's theorem, and the electric field of a charged wire. Ideal for students studying electric phenomena in physics.

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