AP Physics 2:: Electric Force Field Potential

What is ELECTRIC POTENTIAL ENERGY, and how is it analogous to GRAVITATIONAL POTENTIAL ENERGY (from the earlier Energy unit), specifically regarding energy stored due to an object's POSITION within a field?

- **A)** Electric potential energy is the energy a CHARGED object possesses due to its POSITION within an electric field -- directly analogous to how gravitational potential energy depends on an object's position (height) within a gravitational field
- **B)** Electric potential energy has no actual relationship to an object's position within an electric field
- **C)** Electric potential energy is IDENTICAL to kinetic energy, with no actual distinction between the two concepts
- **D)** Electric potential energy depends only on an object's MASS, with no actual relationship to electric charge or field position

What is ELECTRIC POTENTIAL (also called VOLTAGE, as introduced in the earlier DC Circuits unit), and what is its mathematical RELATIONSHIP to electric potential ENERGY and CHARGE?

- **A)** This concept has no actual mathematical relationship between electric potential, potential energy, and charge
- **B)** Electric potential is calculated as V = PE*q (potential energy multiplied by charge), rather than divided by charge
- **C)** Electric potential is the electric potential ENERGY per unit CHARGE at a given point; V = PE/q, measured in VOLTS (joules per coulomb) -- this directly extends the voltage concept from the DC Circuits unit to a more general, point-in-space definition
- **D)** Electric potential depends only on charge, with no actual relationship to potential energy

What is the mathematical FORMULA for the ELECTRIC POTENTIAL produced by a SINGLE point charge, at a distance r from that charge?

- **A)** This concept has no actual mathematical relationship between electric potential and the source charge or distance
- **B)** Electric potential from a point charge is always ZERO, regardless of the charge or distance
- **C)** V = k*q/r, where k is Coulomb's constant and q is the source charge -- unlike electric FIELD (which is a VECTOR and depends on 1/r^2), electric POTENTIAL is a SCALAR and depends on 1/r (not 1/r^2)
- **D)** V = k*q/r^2 (identical to the electric field formula), rather than the correct 1/r dependence for potential

Why is ELECTRIC POTENTIAL a SCALAR quantity, while ELECTRIC FIELD is a VECTOR quantity, and what practical CONSEQUENCE does this have when calculating the NET potential (or field) from MULTIPLE point charges?

- **A)** Since electric potential is a SCALAR (having only magnitude and sign, no direction), the net potential from multiple charges is found by simple ALGEBRAIC addition (accounting for positive/negative signs) -- in contrast, electric FIELD (a vector) requires more complex VECTOR addition, accounting for both magnitude AND direction
- **B)** Electric potential is actually a VECTOR quantity, identical to electric field, with no actual distinction between the two in terms of scalar versus vector nature
- **C)** This concept has no actual relationship between electric potential's scalar nature and how multiple charges' potentials are combined
- **D)** Combining multiple charges' contributions to net potential requires the SAME complex vector-addition process as combining electric fields, with no actual simplification from potential being scalar

What is the mathematical RELATIONSHIP between ELECTRIC FIELD and ELECTRIC POTENTIAL in a UNIFORM electric field (like between two parallel plates), specifically regarding the field magnitude, the potential DIFFERENCE, and the DISTANCE between two points?

- **A)** Electric field magnitude is always INDEPENDENT of potential difference, regardless of the distance between two points
- **B)** For a uniform electric field, E = delta_V/d (electric field magnitude equals the potential difference divided by the distance between two points along the field direction) -- this formula directly connects the field and potential descriptions for the important special case of a uniform field
- **C)** E = delta_V*d (multiplying rather than dividing potential difference by distance), rather than the correct division
- **D)** Electric field and potential difference have no actual mathematical relationship to each other, even in a uniform field

In which DIRECTION does the ELECTRIC FIELD point RELATIVE to regions of HIGH versus LOW electric potential -- does the field point from HIGH to LOW potential, or from LOW to HIGH potential?

- **A)** The electric field points in the direction of DECREASING electric potential -- from regions of HIGHER potential toward regions of LOWER potential (this is analogous to how gravitational field/force points from high gravitational potential energy toward low potential energy, i.e., 'downhill')
- **B)** Electric field direction has no actual relationship to regions of high or low electric potential
- **C)** Electric field direction is completely independent of potential, pointing in a random direction unrelated to potential gradients
- **D)** The electric field points from LOW potential toward HIGH potential, the reverse of the actual relationship

What is an EQUIPOTENTIAL SURFACE (or, in two dimensions, an EQUIPOTENTIAL LINE), and what is the geometric RELATIONSHIP between equipotential surfaces and ELECTRIC FIELD LINES?

- **A)** This concept has no actual geometric relationship between equipotential surfaces and electric field lines
- **B)** Equipotential surfaces only exist for POINT charges, with no actual applicability to other charge configurations like parallel plates
- **C)** Equipotential surfaces are always PARALLEL to electric field lines, rather than perpendicular to them
- **D)** An equipotential surface is a surface on which EVERY point has the SAME electric potential; equipotential surfaces are always PERPENDICULAR to electric field lines at every point where they intersect

Why does NO WORK need to be done to move a charge ALONG an EQUIPOTENTIAL SURFACE (from one point to another point on the SAME surface)?

- **A)** Work is required to move a charge along an equipotential surface, but only if the charge is NEGATIVE, not if it is positive
- **B)** Moving a charge along an equipotential surface always requires a LARGE amount of work, contradicting the actual zero-work property
- **C)** Since every point on an equipotential surface has the SAME electric potential (by definition), moving a charge between any two points on that surface produces ZERO CHANGE in potential energy (delta_PE = q*delta_V = q*0 = 0), and therefore requires ZERO net work against the electric force
- **D)** This concept has no actual relationship between an equipotential surface and the work required to move a charge along it