3 questions about Potential difference equation

1. An electric charge is moved in a homogeneous electric field with a force of 2√3 N a distance of 20 cm. If the direction of the force is at an angle of 30^{o} to the displacement of the electric charge, what is the difference in the electric potential energy at the initial and final positions of the electric charge.

__Known:__

Force (F) = 2√3 N

Distance (s) = 20 cm = 0.2 m

Angle (θ) = 30^{o}

__Wanted:__ Electric potential difference

__Solution:__

The work of transferring charge +q from a to b is equal to the electric potential energy difference at points a and b.

ΔEP = ΔW

If the direction of the force F with respect to the direction of charge transfer +q is angled θ, then the work of charge transfer +q from a to b is:

ΔW = F Δs cos θ = (2√3)(0,2)(cos 30) = (0,4√3)(0,5√3) = (0,2)(3) = 0,6 Joule

2. If the charge and capacity of the capacitor are known to be 5 µC and 20 µF, respectively, determine the potential difference of the capacitors.

__Known:__

Electric charge (q) = 5 µC = 5 x 10^{-6} C

Capacitor capacity (C) = 20 µF = 20 x 10^{-6} F

__Wanted:__ Capacitor potential difference (V)

__Solution:__

The formula for capacitor potential difference, capacitor capacity and charge:

V = q / C = (5 x 10^{-6}) / 20 x 10^{-6} = 5/20 = 0,25 Volt

3. Two point charges QA = -4 µC and QB = 8 µC are 16 cm apart. Determine the electric potential at a point halfway between the two charges.

__Known:__

Electrical charge 1 (Q_{A}) = 4 x 10^{-6} C

Electrical charge 2 (Q_{B}) = 8 x 10^{-6} C

Distance (r) = 8 cm = 0,08 m

Coulomb constant (k) = 9 × 10^{9} Nm^{2}/C^{2}

__Wanted:__ The electric potential at C (V_{C})

__Solution:__

V_{A} = k Q / r = (9 × 10^{9})(4 x 10^{-6}) / 0,08 = (36 × 10^{3}) / 0,08 = -450 Volt

V_{B} = k Q / r = (9 × 10^{9})(8 x 10^{-6}) / 0,08 = (72 × 10^{3}) / 0,08 = 900 Volt

The electric potential at C (V_{C}) = 900 – 450 = 450 Volt

**20 conceptual questions and answers related to potential difference.**

**Question:**What is potential difference?**Answer:**Potential difference, also known as voltage, is the work done per unit charge to move a positive charge from one point to another within an electric field.**Question:**What is the unit of potential difference?**Answer:**The unit of potential difference in the International System of Units (SI) is the Volt (V), which is equivalent to one Joule per Coulomb (J/C).**Question:**How is potential difference related to electric field and distance?**Answer:**Potential difference (V) is related to the electric field (E) and distance (d) by the equation V = E x d.**Question:**Can potential difference exist without current?**Answer:**Yes, potential difference can exist without current. For example, there can be a potential difference across the terminals of a battery even when it is not connected to a circuit.**Question:**How is potential difference related to energy?**Answer:**Potential difference is the work done to move a unit positive charge from one point to another. Thus, it is a measure of the potential energy per unit charge. The work done in moving a charge in an electric field corresponds to a change in this potential energy.**Question:**Is potential difference a scalar or vector quantity?**Answer:**Potential difference is a scalar quantity. It does not have a direction associated with it.**Question:**Can potential difference be negative?**Answer:**Yes, potential difference can be negative. A negative potential difference indicates that work is done by the charge, rather than on the charge, as it moves in the electric field.**Question:**How is potential difference measured?**Answer:**Potential difference is typically measured with a device called a voltmeter, which is connected in parallel across the two points in question.**Question:**What is the potential difference across a resistor in terms of current and resistance?**Answer:**According to Ohm’s Law, the potential difference (V) across a resistor is equal to the product of the current (I) through the resistor and the resistance (R) of the resistor. This is represented by the equation V = I x R.**Question:**What happens to the potential difference across a component if the current through it is doubled?**Answer:**If the resistance remains constant, then according to Ohm’s law, doubling the current will double the potential difference across the component.**Question:**How does potential difference relate to electric power?**Answer:**Electric power (P) is the product of potential difference (V) and current (I), as given by the equation P = V x I.**Question:**What is the effect of a potential difference on free electrons in a conductor?**Answer:**A potential difference applied across a conductor provides an electric field that exerts a force on free electrons, causing them to move and thus creating an electric current.**Question:**How does the potential difference across elements in series compare?**Answer:**For elements connected in series, the total potential difference across all elements is the sum of the potential differences across each element.**Question:**How does the potential difference across elements in parallel compare?**Answer:**For elements connected in parallel, the potential difference across each element is the same.**Question:**What is the potential difference across a short circuit?**Answer:**The potential difference across a short circuit is zero, as there is no resistance to the flow of current.**Question:**How does potential difference relate to electric potential energy?**Answer:**Electric potential difference is the change in electric potential energy per unit charge.**Question:**What is the role of a battery in creating potential difference in a circuit?**Answer:**A battery converts chemical energy into electrical energy, creating a potential difference between its terminals that can drive current through a circuit.**Question:**Can potential difference exist in a superconductor?**Answer:**No, in a superconductor, which has zero resistance, there cannot be a potential difference as long as it remains in the superconducting state.**Question:**What is the effect of the potential difference on the speed of electrons in a conductor?**Answer:**The potential difference does not affect the average speed of electrons, also known as drift speed, in a simple conductive wire. The drift speed depends on the current and the properties of the wire. However, a higher potential difference does make the electrons move back and forth more quickly, and thus they collide with the atoms of the conductor more often, which leads to resistance.**Question:**How does the potential difference affect the brightness of a bulb in a circuit?**Answer:**The potential difference across a bulb affects its brightness. A higher potential difference leads to a larger current and thus more power being dissipated in the bulb, making it brighter.