WorksheetsElectric Fields and Gauss's Law Concepts
Total questions: 45
Worksheet time: 2hrs 30mins
Inside a uniformly charged conducting shell, the electric field is
Zero everywhere inside
Constant everywhere inside
Inversely proportional to r² inside
Directed radially outward, increasing with r
The main reason Gauss’s law is powerful for an infinite line of charge is
The line produces no electric field
The symmetry makes the field constant on the Gaussian surface
The field strength does not depend on distance
Charges cancel out everywhere
If you double the radius of a spherical Gaussian surface while keeping the enclosed charge fixed, the electric flux through the surface
Doubles
Quadruples
Stays the same
Goes to zero
A proton moves in the direction of a uniform electric field. What happens?
Potential energy increases, kinetic decreases
Potential energy decreases, kinetic increases
Both potential and kinetic increase
Both potential and kinetic decrease
Two point charges are separated by a distance r. If you double the separation, the potential energy
Doubles
Halves
Becomes zero
Remains constant
Why is the electric field always perpendicular to equipotential surfaces?
Otherwise charges would stop moving
Otherwise the surface would have thickness
Otherwise there would be work done along the surface
Otherwise the charge density would change
Inserting a dielectric between capacitor plates increases capacitance because
It increases the distance between plates
It cancels the electric field inside the dielectric
It reduces the effective field, allowing more charge storage
It increases the voltage across the plates
Doubling the plate area of a parallel-plate capacitor (with same separation) will
Double the electric field, double the capacitance
Leave the electric field the same, double the capacitance
Halve the electric field, leave capacitance unchanged
Double both the field and stored energy
A dipole placed in a uniform electric field experiences
Net force but no torque
Torque but no net force
Both torque and net force
Neither torque nor net force
Why does the field of a dipole fall off faster (∝ 1/r³) than that of a point charge (∝ 1/r²)?
Dipole fields cancel more at long range
Dipoles have less charge
Gauss’s law doesn’t apply to dipoles
The dipole field is always weaker
If a Gaussian surface encloses no net charge, then
The field everywhere on the surface must be zero
The flux through the surface is zero
The flux through the surface must be positive
The enclosed charge must still be nonzero
A cube is placed in a uniform electric field. The net flux through the cube is
Zero
Positive
Negative
Cant be found
Why do physicists often use electron-volts (eV) instead of joules?
Joules are too small to measure accurately
eV directly relate energy to charge and potential difference
Joules are not SI units
eV are only used for photons
An electron and a proton are initially 1.0 m apart. If the electron is moved to be 0.25 m from the proton, what happens to the magnitude of the electrostatic force on the proton?
It increases to 4× the original.
It increases to 2× the original.
It increases to 16× the original.
It decreases to ¼ of the original.
Four charges sit at the corners of a square of side a: B and C are +1.0 C (opposite corners). A and D are on the other two corners. What charge must A carry so that the net Coulomb force on B is zero? (Assume D has the same charge as A.)
+1.0 C
−1.0 C
−2√2 C
+2√2 C
Two equal and opposite charges +Q and −Q are placed at x = +d and x = −d on the x-axis. At a point on the +y axis (0, y) with y ≫ d, the electric field vector points
Straight upward (+y)
Straight downward (−y)
Along +x (right)
Along −x (left)
An uncharged hollow conductor contains a point charge +q inside the cavity (not touching). There are no other charges. Which statement is true?
Inner surface has +q and outer surface has 0.
Inner and outer surfaces each have −q/2.
The conductor material has a nonzero E-field pointing away from +q.
Outer surface has +q and inner surface has −q.
Both surfaces carry no excess charge.
A long conducting cylinder (rod) of radius R and length H (H ≫ R) actually carries a total linear charge density λ (on its surface). Consider a coaxial Gaussian cylinder of radius r₁ < R and length H (inside the conductor). What is the electric flux through that inner Gaussian surface?
(λH/ε₀)·(r₁/R)²
(λH/ε₀)·(r₁/R)
(λH)·(r₁/R)
(r₁/R)·λH
Zero
For the outside surface at r = r₂ (r₂ > R), the magnitude of the electric field at that surface is
(1 / 4π ε₀) · (λ / r₂²)
(1 / 2π ε₀) · (λ / r₂)
Zero
(1 / ε₀) · (1 / R)
Two point charges, q₁ = +1.60×10⁻¹⁹ C and q₂ = −1.60×10⁻¹⁹ C, are separated by 5.00×10⁻¹⁰ m (approx. atomic scale). What is the magnitude of the force that one exerts on the other?
7.65×10⁻¹⁰ N
7.97×10⁻¹⁰ N
8.24×10⁻¹⁰ N
8.86×10⁻¹⁰ N
9.20×10⁻¹⁰ N
A dipole p (with moment magnitude p) lies in a uniform E-field. The torque magnitude on the dipole is
pE cosθ
pE sinθ
pE / r²
pE²
A point charge +Q is at the origin. A dipole with +q at x = 10.0×10⁻¹⁰ m and −q at x = 15.0×10⁻¹⁰ m lies on the +x axis. What is the magnitude of the net force on the dipole due to the origin charge? (Use q = 1.60×10⁻¹⁹ C; present choices are approximate.)
1.08×10⁻¹⁰ N
1.28×10⁻¹⁰ N
1.69×10⁻¹⁰ N
1.90×10⁻¹⁰ N
Two small identical conducting spheres, each carrying charge +Q, are touched together and then separated again. Which of the following describes the final charges on each sphere?
One sphere has +2Q, the other 0.
Each sphere has +Q (unchanged).
Each sphere has +Q/2.
Each has +2Q.
A 10.0 g pith ball carries a charge of +1.52 μC and hangs from a 25.0 cm thread in equilibrium at angle θ from vertical because of the electric force from a charged vertical wall (σ = +3.57 μC/m²). Which of the following must be true about the electric field from the wall at the ball’s location (neglect gravity for this statement)?
The field points horizontally away from the wall and has magnitude σ/2ε₀.
The field points horizontally toward the wall and has magnitude σ/2ε₀.
The field points horizontally away from the wall and has magnitude σ/ε₀.
The field is zero because the wall is infinitely wide.
An electron is accelerated from rest through a potential difference of 200 V. What is its kinetic energy after acceleration?
1.6×10−17J
3.2×10−17J
1.6×10−19J
3.2×10−19J
The torque on an electric dipole in a uniform electric field is maximum when the dipole moment is
Parallel to the field
Perpendicular to the field
Anti-parallel to the field
Zero
When a dielectric material is placed between capacitor plates
The electric field increases
The capacitance decreases
Bound charges form on the surfaces of the dielectric
The potential difference between the plates increases
A proton is released from rest at a point with electric potential of 120 V and moves to a region of 60 V. Its change in potential energy is
−9.6×10−18J
+9.6×10−18J
−1.9×10−17J
+1.9×10−17J
The angle between a uniform electric field and a surface area vector is 60°. If the field has magnitude E and the surface area is A, the flux is
EA
EAsin60∘
EAcos60∘
Zero
Which of the following correctly defines the electromotive force (emf) of a battery?
The energy per unit charge supplied by the battery.
The current supplied by the battery.
The maximum power delivered to the circuit.
The potential difference across the battery when current flows.
A hollow conducting sphere is given a net charge +Q. A point charge +q is then placed at the exact center inside the cavity. What is the net charge on the outer surface of the conductor?
+Q
+Q + q
+Q − q
+q
A Gaussian surface encloses a dipole consisting of +q and −q separated by distance d. The net electric flux through the Gaussian surface is
Proportional to 1/d²
Zero
Equal to (q/ε₀)
Depends on the dipole orientation
A proton and an electron are placed in a uniform electric field. Ignoring gravity, which statement is true about their accelerations?
They have the same magnitude and direction.
They have the same magnitude but opposite directions.
The proton accelerates faster.
The electron accelerates faster.
Two capacitors are connected in parallel, one with a dielectric and one without. A battery is connected across them. Compared to the capacitor without dielectric, the capacitor with dielectric has
The same voltage but more charge stored.
A smaller voltage but the same charge.
A larger voltage but less charge stored.
The same charge stored regardless of dielectric.
An infinitely long, uniformly charged line produces an electric field proportional to
1/r²
1/r
log(r)
Constant (independent of r)
A grounded conducting plane lies at x = 0. A point charge +q is placed at (a, 0). The method of images can be used to replace the plane with an image charge located at
(−a, 0) with charge +q
(−a, 0) with charge −q
(a, 0) with charge −q
(−a, 0) with charge −2q
The electric potential inside a uniformly charged non-conducting solid sphere of total charge Q and radius R varies with distance r (from the center) as
V ∝ 1/r
V ∝ r²
V ∝ constant − (r²)
V ∝ constant − (1/r²)
Which of the following situations produces the largest electric field at the center of a square of side a? Charges are placed at the four corners:
All four charges are +Q.
Two opposite corners are +Q, the other two are −Q.
Adjacent corners are +Q, the other two are −Q.
Diagonal corners are +Q, the other two are neutral.
If a region of space has zero electric potential everywhere, which of the following must also be true?
The electric field in that region is zero.
The charge density in that region is zero.
Both electric field and charge density are zero.
Neither electric field and charge density are zero.
A spherical conducting shell carries net charge +Q. A charge −q is placed outside the shell. The induced charge on the inner surface of the shell is
Zero
+q
−q
Depends on the distance of −q from the shell
The SI unit of the electric field can be expressed as
J/C
N/C
V/m
Both B and C
The electric field strength between two parallel plates separated by 0.020 m is 300 V/m. What potential difference is applied across the plates?
6.0 V
15 V
60 V
150 V
Which of the following is not a valid unit for the electric field?
N/C
J/C·m
V/m
C/N
If a charge of 2.0 μC experiences a force of 0.060 N in a uniform electric field, what is the magnitude of the electric field?
1.2 × 10⁴ V/m
3.0 × 10⁴ V/m
6.0 × 10⁴ V/m
1.2 × 10⁵ V/m
Which dimensional formula correctly represents the electric field (E)?
[M L T⁻³ I⁻¹]
[M L T⁻² I⁻¹]
[M L⁻¹ T⁻² I]
[M L² T⁻³ I]
