Gausss Law
A solid insulating sphere of radius R carries a total charge Q distributed uniformly throughout its volume. A Gaussian surface is drawn at radius r = R/2. What fraction of the total charge Q is enclosed by this Gaussian surface?
A physicist places a point charge of +5.0 μC inside an irregularly shaped closed surface. She then replaces that surface with a perfect sphere of twice the radius that also encloses only the same charge. How does the total electric flux through the new spherical surface compare to the flux through the original irregular surface?
An infinite straight wire carries a uniform linear charge density λ = 4.0 × 10⁻⁸ C/m. Calculate the electric field at a perpendicular distance of 0.20 m from the wire.
A solid insulating sphere of radius R = 0.20 m has total charge Q = 8.0 × 10⁻⁶ C distributed uniformly. What is the electric field at r = 0.10 m from the center?
An engineer designs a sensor using two large parallel non-conducting sheets. Sheet 1 has surface charge density +σ and Sheet 2 has surface charge density −σ. A dust particle carrying charge q = +2.0 × 10⁻⁹ C is suspended motionless between the sheets against gravity. If the particle has mass m = 5.0 × 10⁻⁶ kg, determine the surface charge density σ. (Take g = 9.8 m/s².)
A conducting spherical shell of radius R carries total charge +Q. Which statement correctly describes the electric field at a point inside the shell at distance r < R from the center?
A solid insulating sphere of radius R = 0.10 m carries a non-uniform volume charge density ρ(r) = βr, where β = 5.0 × 10⁻⁵ C/m⁴. What is the total charge enclosed by a Gaussian sphere of radius r = 0.060 m?
Which of the following Gaussian surfaces is most appropriate for determining the electric field at a perpendicular distance d from an infinite uniformly charged plane?
A spacecraft electronics bay is modeled as a conducting spherical shell of radius 0.50 m carrying a net charge of +12 μC. A technician needs to know the electric field just outside the shell. An intern calculates the field using E = kQ/R (forgetting to square the radius). What is the correct electric field just outside the shell?
Two infinitely large parallel non-conducting sheets both carry surface charge density +σ. What is the electric field in the region between the two sheets?
A point charge Q = +3.0 × 10⁻⁶ C is located at the center of a cube with side length 0.40 m. What is the total electric flux through one face of the cube?
A Gaussian surface encloses three charges: +4.0 μC, −7.0 μC, and +2.0 μC. A fourth charge of +5.0 μC sits outside the surface. What is the total electric flux through the Gaussian surface?
An insulating sphere of radius R has a uniform volume charge density ρ. At what radial distance from the center does the electric field reach its maximum value?
A student claims: “If the net electric flux through a closed surface is zero, there can be no charges anywhere inside.” Determine whether this claim is correct and justify your reasoning.
A long conducting cylinder of radius R carries charge per unit length λ. At what distance from the axis is the electric field exactly half the value at the surface?
A solid insulating sphere of radius R = 0.15 m carries uniform volume charge density ρ = 2.0 × 10⁻⁶ C/m³. Calculate the total electric flux through a concentric Gaussian sphere of radius r = 0.090 m.
A thundercloud can be roughly modeled as two large parallel plates: the cloud base at negative charge density −σ and the ground below at induced positive charge density +σ. If the electric field between cloud and ground is 3.0 × 10⁵ N/C (roughly the breakdown field of air), what is the magnitude of σ on each surface?
A hollow conducting sphere of inner radius a and outer radius b has a point charge +q placed at its center. What is the total charge on the inner surface of the conductor?