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Calculate the electric voltage at a point
Electric voltage
Definition: The work needed to move a unit positive charge from infinity to the desired point.
Electric Potential of a Point Charge
\[ V = k \frac{Q}{r}\] ➔
\[ V = (8.99×10^9)×\frac { Q }{ r}\]
Properties of Electric Potential:
- Scalar quantity (has magnitude only)
- Depends on the distance from the charge
- Measured in Volt (V)
Practical Example:
A point charge
\[ Q = +5\;nC\]
Find the electric potential at a distance
\[r= 0.3\;m \]
Potential calculation:
\[V = (8.99×10^9) × \frac {5×10^{-9}}{0.3}\]
\[V = 149.83 V \]
Electric Potential Calculation
Point Charge Electric Potential Calculator
Notes:
- Potential equation: \[V =\frac { k * Q }{ r}\]
- k: Coulomb's constant
\[k=(8.99×10^9)N.m^2/c^2\]
- Q: Charge value in Coulombs
- r: Distance from charge in meters
- Result appears in scientific notation (example: 1.23e+5)
Electric Potential of Point Charges
Electric Potential of Multiple Point Charges
Basic Concept:
The electric potential (V) at a point in space is the amount of work needed to move a unit positive test charge from infinity to that point without acceleration.
For a single point charge:
\[ V =k *\frac { q }{ r}\]
Where:
- k Coulomb's constant
\[k=(8.99×10^9)N.m^2/c^2\]
- q: Charge amount (Coulombs)
- r: Distance from charge to the studied point (meters)
For multiple point charges:
\[ V_{total} = Σ V_i = k Σ\frac {q_i}{r_i}\]
Total potential is calculated by algebraic sum of individual potentials for each charge (superposition principle)
Calculation importance:
- Design of electronic circuits and electrical complexes
- Analysis of charge systems in capacitors
- Study of electric fields in biological systems (e.g., ECG devices)
- Applications in X-ray systems and microelectronics
Practical applications:
- Design of electrostatic storage devices
- Calculation of capacitor capacitance
- Analysis of heart electrical signals
- Lightning protection systems
- Electron beams in cathode ray tubes
Important notes:
- Potential is a scalar quantity (not vector) → easier to calculate
- Positive charges produce positive potentials
- Negative charges produce negative potentials
- Measurement unit: volt (1 volt = 1 joule/coulomb)
Electric Potential Calculator
Electric Potential Calculator
Charge (µC):
Distance (m):
Uniform Electric Potential
Uniform Electric Potential
Scientific Concept:
Uniform electric potential occurs when the electric field is constant in magnitude and direction, resulting in a linear change in electric potential with distance.
Mathematical Relationship:
\[ ΔV = -E × d × cosθ\]
Where:
- ΔV: Potential difference (Volts)
- E: Electric field intensity (Volts/meter)
- d: Distance (meters)
- θ: Angle between field direction and motion direction
Affecting Factors:
- Electric field intensity (E)
- Distance traveled (d)
- Direction of motion relative to the field (θ)
Practical Example:
If there is a uniform electric field with intensity
\[E=50 \;v/m\]
and a charge is moved 3 meters parallel to the field, the potential difference would be
\[ ΔV = -(50) × 3 × cos(0°) = -150\; V\]
Key Properties:
- Linear change in potential with distance
- Direction of steepest potential decrease matches electric field direction
- Equipotential surfaces are parallel and evenly spaced
- Electric field is the negative spatial gradient of potential (E = -∇V)
Important Notes:
1. The negative sign reflects the direction of potential decrease
2. Potential increases when moving against the field
3. No potential change occurs when moving perpendicular to the field (θ = 90°)
Calculate the electric voltage at a point |
Electric voltage
Definition: The work needed to move a unit positive charge from infinity to the desired point.
Electric Potential of a Point Charge
\[ V = k \frac{Q}{r}\] ➔
\[ V = (8.99×10^9)×\frac { Q }{ r}\]
Properties of Electric Potential:
- Scalar quantity (has magnitude only)
- Depends on the distance from the charge
- Measured in Volt (V)
Practical Example:
A point charge \[ Q = +5\;nC\] Find the electric potential at a distance \[r= 0.3\;m \]
Potential calculation:
\[V = (8.99×10^9) × \frac {5×10^{-9}}{0.3}\]
\[V = 149.83 V \]
Point Charge Electric Potential Calculator
Notes:
- Potential equation: \[V =\frac { k * Q }{ r}\]
- k: Coulomb's constant \[k=(8.99×10^9)N.m^2/c^2\]
- Q: Charge value in Coulombs
- r: Distance from charge in meters
- Result appears in scientific notation (example: 1.23e+5)
Electric Potential of Multiple Point Charges
Basic Concept:
The electric potential (V) at a point in space is the amount of work needed to move a unit positive test charge from infinity to that point without acceleration.
For a single point charge:
Where:
- k Coulomb's constant
\[k=(8.99×10^9)N.m^2/c^2\]
- q: Charge amount (Coulombs)
- r: Distance from charge to the studied point (meters)
For multiple point charges:
Total potential is calculated by algebraic sum of individual potentials for each charge (superposition principle)
Calculation importance:
- Design of electronic circuits and electrical complexes
- Analysis of charge systems in capacitors
- Study of electric fields in biological systems (e.g., ECG devices)
- Applications in X-ray systems and microelectronics
Practical applications:
- Design of electrostatic storage devices
- Calculation of capacitor capacitance
- Analysis of heart electrical signals
- Lightning protection systems
- Electron beams in cathode ray tubes
Important notes:
- Potential is a scalar quantity (not vector) → easier to calculate
- Positive charges produce positive potentials
- Negative charges produce negative potentials
- Measurement unit: volt (1 volt = 1 joule/coulomb)
Electric Potential Calculator
Uniform Electric Potential
Scientific Concept:
Uniform electric potential occurs when the electric field is constant in magnitude and direction, resulting in a linear change in electric potential with distance.
Mathematical Relationship:
\[ ΔV = -E × d × cosθ\]
Where:
- ΔV: Potential difference (Volts)
- E: Electric field intensity (Volts/meter)
- d: Distance (meters)
- θ: Angle between field direction and motion direction
Affecting Factors:
- Electric field intensity (E)
- Distance traveled (d)
- Direction of motion relative to the field (θ)
Practical Example:
If there is a uniform electric field with intensity
\[E=50 \;v/m\]
and a charge is moved 3 meters parallel to the field, the potential difference would be
\[ ΔV = -(50) × 3 × cos(0°) = -150\; V\]
Key Properties:
- Linear change in potential with distance
- Direction of steepest potential decrease matches electric field direction
- Equipotential surfaces are parallel and evenly spaced
- Electric field is the negative spatial gradient of potential (E = -∇V)
Important Notes:
1. The negative sign reflects the direction of potential decrease
2. Potential increases when moving against the field
3. No potential change occurs when moving perpendicular to the field (θ = 90°)
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