Electrostatics Practice Test

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• Is the following statement true or false? In a linear dielectric, the energy density can also be written as u = 1/2 ε E^2.
• During charging by induction, which sequence is correct?
• A capacitor charged to Q0 and V0 is isolated from the source and the dielectric is inserted (κ). What happens to the voltage across the plates?
• Two point charges q1 = 2 μC and q2 = 3 μC are separated by d = 0.5 m. Using k = 9 x 10^9 N m^2/C^2, what is the magnitude of the electrostatic force between them?
• What is the electric potential at distance r from a point charge q (with V(∞) = 0)?
• A parallel-plate capacitor with plate area A and separation d in vacuum carries charges ±Q. Which set of expressions correctly gives its capacitance C and the potential difference V?
• Which particle carries a negative elementary charge?
• For a solid sphere with total charge Q, what is the electric field outside the sphere for r > R?
• Across a dielectric boundary with no surface current, what is true about the tangential component of the electric field E_t?
• Which statement correctly contrasts conductors, insulators, and semiconductors?
• On the axis of a uniformly charged disk, what is E_z at z = 0?
• A capacitor with capacitance 2 μF is charged to 5 V. What is the energy stored in the capacitor?
• If the same setup as above but the distance between the charges is now three times greater, how does the force compare to its original value?
• A hollow conducting shell carries total charge Q. What is the field in the region outside the shell (r > R)?
• State the energy density in a vacuum and in a linear dielectric in terms of E and D.
• Inside a conductor placed in a static external electric field, what is the electric field in the conductor's interior?
• During charging by induction, which component is grounded?
• Which statement best distinguishes free charge from bound charge?
• What do electric field lines illustrate about the field?
• Which equation represents Gauss's law in integral form?
• Which expression correctly represents the electric energy density in vacuum?
• If distance between two charges doubles, the force magnitude becomes
• Electric field due to an infinite line of charge with linear density λ at distance r from the line is:
• Which expression correctly gives the energy stored in a capacitor in terms of its capacitance C and voltage V?
• If the distance between two charges is halved, what happens to the electric force?
• Which expression gives the energy stored in a capacitor in terms of capacitance C and voltage V?
• State the energy stored in a capacitor in terms of Q and C.
• Capacitance is defined as the charge stored per volt. What is the unit of capacitance?
• Which device is used to measure electrical potential difference?
• A capacitor is connected to a fixed-voltage source V. If a dielectric with dielectric constant κ is inserted between plates, how do C, Q, and V change?
• Which of the following is a method of charging an object by direct contact?
• One microcoulomb equals
• The electric field due to a positive point charge is directed...
• How is capacitance C defined?
• Using the method of images, a point charge q at distance d from an infinite grounded conducting plane experiences what force magnitude and direction?
• What happens when you unscrew a bulb in a mixed circuit, according to the source?
• What is the equivalent capacitance of N identical capacitors in parallel?
• Which statement about electric forces is always true?
• What is the energy stored in a charged capacitor?
• Electric field lines are used to represent the field produced by a point charge. Which of the following is true about field lines?
• State Gauss's law in differential form.
• How does the dielectric constant κ affect the capacitance for a capacitor with fixed geometry?
• For a point dipole with moment p, the potential at distance r and angle θ between p and r̂ is what?
• Which expression is also a valid form for the energy stored in a capacitor?
• Coulomb's constant k has the value
• N identical capacitors in series have Ceq equal to C/N. Which expression correctly gives the equivalent capacitance?
• Which statement best describes how capacitance changes with plate area and separation?
• In electrostatic equilibrium, what is the electric field inside a conductor?
• In the Coulomb force expression F12 = k q1 q2 / r^2 r_hat_12, the unit vector r_hat_12 points from which to which?
• Write the potential at a point P due to two point charges q1 at r1 and q2 at r2.
• The work required to assemble two charges q1 and q2 from infinity to separation r12 is:
• Which statement about electric field lines is true?
• Electric field due to an infinite plane sheet of charge with surface density σ. Which expression describes the field on either side of the sheet?
• Which symbol is commonly used to denote electric charge in equations?
• What is the electric field produced by a single point charge q at distance r?
• Which is the SI unit of electric charge?
• Electric field inside a uniformly charged solid sphere of radius R and total charge Q at distance r < R from the center is given by which expression?
• In a linear dielectric, which expression correctly relates the displacement field D to the electric field E and the permittivity?
• What is the potential energy U of two point charges q1 and q2 separated by distance r12?
• An electric dipole consists of two charges ±q separated by distance d; which pair of expressions correctly gives the dipole moment p and the potential energy in a uniform external field?
• Charging by conduction occurs when a charged object does what to a neutral object?
• For a uniformly charged spherical shell, which statement about the potential inside the shell is true?
• A cylindrical capacitor has length L, inner radius A, outer radius B. What is its capacitance?
• Define free charge and bound charge; express bound charges in terms of polarization P.
• State Gauss's law in integral form.
• There are two types of electric charges. Which are they?
• A test charge q is moved through a potential difference ΔV by an external agent. What is the work done by the external agent?
• In a mixed circuit, removing a bulb can cause the remaining bulb to brightness change in what way according to the source?
• Far from a static electric dipole, what is the electric field on the dipole axis (θ = 0) at large distance r?
• Which type of material allows charges to move freely?
• How does Gauss's law utilize symmetry to find electric fields?
• Field on axis of a uniformly charged ring of radius a with total charge Q at axial distance z. Which expression is correct?
• Which expression correctly gives the energy stored in a capacitor when the capacitance is C and the voltage across it is V?
• Along the axis of a point dipole with moment p at distance r, what is the leading-order expression for the far-field electric field?
• Which equation correctly relates work, charge, and potential difference?
• What does the conservation of charge state about the net charge of an isolated system?
• Electric field just outside a charged conductor is perpendicular to the surface.
• In the far field of a point dipole, how does the potential V fall off with distance r?
• The electric field just outside the surface of a conductor is directed how relative to the surface?
• Field inside a thin spherical shell of radius R carrying total charge Q. Which statement is correct?
• If a small amount of negative charge is placed near a neutral hollow metal sphere, where does the excess charge distribute seconds later?
• What is a capacitor primarily used for?
• In a simple parallel circuit with two identical bulbs, how does their brightness compare?
• If two positively charged particles interact with a net charge of +1 and one particle is replaced by a +4 charge, at the same separation, how does the electrostatic force between them change?
• Which expression best represents the superposition of fields from two charges at a point?
• What are the standard SI units for electric field and potential?
• Which equation correctly relates D, E, and P in a dielectric?
• If a small amount of negative charge is placed near an electrically neutral insulating material, where does the charge reside seconds later?
• Which statement about brightness in a mixed circuit is true according to the material?
• Which statement accurately describes Coulomb's Law?
• What is the direction of the force between two opposite charges?
• What is the work W done by an external agent moving a test charge q from point A to B in an electrostatic field?
• For a uniformly charged hollow spherical shell, what are the electric field values outside and inside?
• For a positive point charge q, what is the potential at distance r from the charge?
• What is the potential inside a uniformly charged spherical shell of radius R and total charge Q?
• A dielectric with dielectric constant κ is inserted between plates of a capacitor that remains connected to a fixed voltage source. What is the effect on the electric field between the plates?
• Which statement best describes polarization P?
• If the plate separation d of a parallel-plate capacitor in vacuum is doubled, what happens to the capacitance?
• In a combined circuit containing a bulb in series with a parallel branch, which bulb tends to be brighter according to the source?
• Millikan's Oil Drop Experiment showed that the elementary charge is the smallest unit of charge; this supports:
• What is the function of an electroscope?
• Which expression gives the force on charge q1 due to charge q2 in the vector form of Coulomb's law?
• For a capacitor, the voltage between plates is V = Q/C. If the charge Q is doubled while the capacitance stays the same, the voltage V:
• What determines the charge stored in a capacitor, according to the source?
• A conductor that is in electrostatic equilibrium has no net motion of its charges.
• For a uniformly charged ring of radius a with total charge Q, when z = 0 along the axis, what is E_z?
• What is the electric energy density u in a vacuum or dielectric?
• The electric field due to a single positive point charge at distance r points in which direction?
• The electric potential at distance r from a point charge q is V(r) = ?
• According to Gauss's law, the electric flux through any closed surface is proportional to which quantity enclosed by that surface?
• A spherical capacitor has inner radius a and outer radius b. What is its capacitance?
• If the plate area is doubled while the distance between plates remains the same, what happens to the capacitance?
• When a dielectric is inserted between the plates while the free charge on the plates remains fixed, how does the electric field change?
• What is the force on a charge q placed in an electric field of strength E?
• Which element is commonly used as a semiconductor in pure form?
• What are the units of the electric field E?
• What is the SI unit of permittivity ε0?
• What is the relation between bound charge density ρ_b and polarization P?
• The displacement field D is related to the vacuum permittivity and polarization by which relation?
• Define electric potential and describe its relation to the electric field.
• Why does the earth accept excess electrons in grounding?
• A proton has what charge?
• Which equation expresses the superposition principle for electric fields?
• Which of the following is the correct vector form of the Coulomb force exerted on q2 by q1?
• Excess charge on an isolated conductor resides entirely on the outer surface.
• Provide the differential relation between electric field and potential.
• Which statement best distinguishes conductors from insulators in electrostatics?
• Apply the superposition principle to two point charges q1 at r1 and q2 at r2: What is the electric field at position r?
• When two conductors touch and have different sizes, how does charge distribute?
• In a linear dielectric, the displacement field D relates to E by D = ε E; what is ε in terms of ε0 and κ?
• State the energy density in a dielectric in terms of E and D.
• Which is the correct vector form of the force on q1 due to q2?
• If a capacitor is connected to a fixed voltage source and a dielectric is inserted, what happens to the capacitance and charge?
• What is the purpose of using a small positive test charge when mapping the electric field?
• If the distance between the plates is halved, what happens to the capacitance?
• What is the torque on a dipole in a uniform external field?
• When a dipole moment p aligns with a uniform external electric field E, what happens to the dipole's potential energy?
• As two like charges are brought closer together, what happens to their potential energy?
• In a circuit with a voltmeter and an ammeter used to measure current and voltage across a resistor, where should the ammeter and voltmeter be placed?
• For a uniformly charged solid sphere with total charge Q and radius R, what is the electric field inside (r < R) and outside (r > R)?
• Which relation defines the electric field?
• Bound surface charge density on a dielectric surface is related to polarization by which expression?
• In a charged capacitor connected to a battery, then disconnected, which statement is true?
• Where are bound charges primarily produced?
• In a series circuit containing a lamp and with no capacitor to store charge, what is the initial behavior when the switch is closed?
• What happens in charge separation by polarization when the external charged object is removed?
• What is the definition of electric flux through a surface?
• If a dielectric of constant κ is inserted into a capacitor that is held at a fixed voltage, what happens to the electric field E and the charge Q?
• Which statement correctly describes the electric field due to an infinite plane sheet of charge with surface density σ?
• Which statement about electrical potential energy in an electric field is true?
• Which statement best defines an equipotential surface?
• Which option describes Charge Separation by Polarization as a charging method?
• Which statement about electric force and gravity is correct?
• A dielectric with constant κ is inserted into a capacitor that is isolated (no connection to a battery), so the charge Q remains fixed. What happens to the capacitance C and the voltage V across the plates?
• In vacuum, the polarization P is zero. Which statement is correct?
• State Gauss's law in terms of D for a dielectric.
• A positively charged particle is released from rest in a uniform electric field. Its subsequent motion is best described as:
• If the voltage across a capacitor is doubled while the capacitance remains the same, by what factor does the stored energy change?
• If two point charges have the same sign, the electrostatic force between them is
• Bound surface charge density on a boundary with polarization P is given by which expression?
• In the image method for a point charge q located at distance d from an infinite grounded conducting plane, the image charge has what magnitude and sign, and where is it located?
• Which expression correctly gives the potential at a point due to two charges q1 and q2 at distances r1 and r2 from the point?
• For a cylindrical capacitor, as the outer radius B becomes much larger than the inner radius A, the factor ln(B/A) grows. What is the qualitative effect on the capacitance C = 2π ε0 L / ln(B/A)?
• If an electron is in a region with an electric potential of +8 V, can its future motion be predicted from this information alone?
• The electric field E at a point is defined as the force on a test charge divided by the test charge. Which statement correctly expresses this relation?
• If you double the plate area and distance between the plates, what happens to capacitance?
• The potential due to a point charge falls off with distance as which function?
• Two identical capacitors, each with capacitance C, connected in series have an equivalent capacitance equal to C/2.
• What is true about semiconductors?
• The field just outside a charged conductor surface with surface charge density σ is:
• As z grows large above a uniformly charged disk, what happens to the axial field E_z?
• In an insulator, where do charges tend to reside?
• What is the correct unit for the electric field?
• A capacitor with plate area A and separation d is filled with a dielectric κ. Provide the capacitance.
• Grounding in electrostatics refers to:
• Which statement best describes the behavior of charge during polarization of an insulator?
• Field inside a long straight cylinder of radius R with uniform volume charge density ρ for r < R. Which expression gives E(r) inside?
• Which statement is true about the relation between D and E in vacuum and in a linear dielectric?
• What is electrostatics?
• Which expression gives the magnitude of the electrostatic force between two point charges according to Coulomb's law?
• What is the electric potential on the surface of a conducting sphere of radius R carrying charge Q in vacuum?
• If you remove a bulb from a mixed circuit, how can the brightness of the remaining bulb change?
• Boundary condition for the normal component of D across an interface with free surface charge density σ_free.
• On axis of a uniformly charged disk of radius R with surface density σ at height z, E_z(z) equals which expression?
• If you double the area AND distance between two circular plates in a capacitor, what happens to the capacitance?
• What is the electric potential just outside a hollow spherical shell of radius R and charge Q at a distance r > R?
• For a cylindrical capacitor with fixed radii, if the length L is doubled, the capacitance:
• What happens to the brightness of the remaining bulbs after unscrewing a bulb in a combined circuit, according to the source?
• In general, which arrangement yields the greatest total current from the battery for a set of resistors?
• How can you compute the energy stored in a capacitor using the electric field?
• Define the polarization P and the displacement D in a linear dielectric, and express D in terms of E and ε.
• What is the boundary condition for E_tangential across a boundary in electrostatics with no time-varying magnetic fields?
• The electric field due to an infinite line charge with linear density λ at distance r is given by which expression?
• What is the electric field just outside each side of an infinite plane sheet with surface density σ?
• If two identical conductive objects touch, how do the charges and voltages distribute?
• The force exerted by q1 on q2 is equal in magnitude and opposite in direction to the force exerted by q2 on q1.
• If a closed surface encloses no net charge, what is the net electric flux through the surface?
• What is polarization P in a dielectric?
• For a positive point charge q, what is the potential at infinity?
• Which statement accurately describes the charges of the fundamental particles?
• Consider a spherically symmetric charge distribution with total charge Q enclosed by a Gaussian surface of radius r > R. What are the electric field E(r) and the electric flux Φ_E through the surface?
• Electric field E is defined as the force Fe on a test charge q0 divided by q0, and its direction corresponds to the force on a positive test charge.
• What is the capacitance of a parallel-plate capacitor (vacuum), and how does a dielectric affect it?
• The energy stored in a capacitor with charge Q and capacitance C is:
• In a uniform electric field, the voltage between two points separated by distance d along the field is equal to:
• What is the energy change when 1 coulomb of charge passes through a potential difference of 1 volt?
• Moving a positive test charge through a uniform electric field, you must do work. What energy change occurs for the test charge?
• Three charges form a triangle: top is positive; bottom left is positive; bottom right is negative with equal magnitudes for bottom charges. What is the horizontal direction of the net force on the top positive charge?
• Which statement about the dependence of U12 on r12 is correct?
• A Faraday cage—a conductor surrounds a region. What is the electric field inside the interior when an external static field is applied?
• For two point charges q1 and q2 separated by r12, what is their electric potential energy U12?
• Inserting a dielectric with dielectric constant κ between the plates of a capacitor affects its capacitance by:
• If a dielectric is inserted into a capacitor with a fixed voltage, the stored energy changes by what factor?
• At a conductor surface, what are the boundary conditions on the electric field immediately outside the surface?
• How does increasing plate area A affect the capacitance of a parallel-plate capacitor at fixed separation and dielectric?
• Charging by friction involves what process?
• Which circuit yields the greatest total current from the battery for the same resistors?
• Gauss's law: what is the electric flux through a closed surface that encloses a total charge Q?
• For a conservative electrostatic field, the potential difference ΔV between two points is related to the electric field by which expression?
• Which scaling describes the far-field axial electric field of a point dipole with moment p at distance r?
• How is the net electric field at a point computed when multiple charges contribute?
• If the capacitance doubles while the voltage remains the same, what happens to the stored energy?
• For a dipole in a uniform external field, if θ = 180 degrees (dipole moment opposite to E), the potential energy is:
• At a boundary with surface free charge density σ_free, which relation describes the normal components of the D field across the boundary?
• An electron has what charge?
• The direction of a field line at a point in space represents
• A capacitor is charged to a voltage V. How does the stored energy change if the voltage is doubled, with the capacitance constant?
• What condition yields zero work when moving a charge between two points on an electrostatic field?
• How is the total electric potential at a point due to multiple point charges computed?
• Which expression correctly gives the energy stored in a capacitor in terms of its capacitance C and voltage V?
• State the energy stored in a capacitor in terms of C and V.
• Inside a long straight cylinder with uniform volume charge density, what is E at the axis r = 0?
• What is the electric field inside a conductor in electrostatic equilibrium?
• What happens to the capacitance when a dielectric fully fills the space between the plates?
• Superconductors are defined as perfect conductors under what condition?