Potential difference equation

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 × 10⁹ Nm²/C²

Wanted: The electric potential at C (V_C)

Solution:

V_A = k Q / r = (9 × 10⁹)(4 x 10^-6) / 0,08 = (36 × 10³) / 0,08 = -450 Volt

V_B = k Q / r = (9 × 10⁹)(8 x 10^-6) / 0,08 = (72 × 10³) / 0,08 = 900 Volt

The electric potential at C (V_C) = 900 – 450 = 450 Volt

20 conceptual questions and answers related to potential difference.

1. 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.
2. 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).
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. Question: How does potential difference relate to electric potential energy? Answer: Electric potential difference is the change in electric potential energy per unit charge.
17. 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.
18. 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.
19. 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.
20. 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.