📄 Print pdf
00971504825082
Electric Field and Potential for Point Charges and Capacitor Plates
Electric Field and Potential for Point Charges
Electric Field and Potential for Point Charges
Electric Field
Definition: The region of space around a charge where electric forces act on other charges.
\[ E = k \frac{Q}{r^2}\] ➔
\[ E = 8.99×10^9 ×\frac { Q }{ r^2}\]
Determining Direction
There are two methods to determine direction
Method 1: Place a test charge at the point where direction needs to be determined
According to vector rules, multiplying a number by a vector
If a positive test charge is placed, the field direction is the same as the force direction
If the test charge is negative, the field direction is opposite to the electric force direction
Method 2: By drawing field lines for positive and negative charges
Field lines for positive charges radiate outward
Field lines for negative charges point inward
Electric Field Properties:
- Vector quantity (has magnitude and direction)
- Created by any electric charge
- Measured in N/C or V/m
Practical Example:
Point charge
\[ Q = +5\;nC\]
Find the electric field at a distance
\[r= 0.3\;m \]
Field calculation (E):
\[E = (8.99×10^9) × \frac {5×10^{-9}}{0.3^2}\]
\[E = 499.4 N/C\]
Electric Potential
Definition: The work needed to move a unit positive charge from infinity to the desired point.
\[ V = k \frac{Q}{r}\] ➔
\[ V = (8.99×10^9)×\frac { Q }{ r}\]
Electric Potential Properties:
- Scalar quantity (magnitude only)
- Depends on distance from the charge
- Measured in Volt (V)
Practical Example:
Point charge
\[ Q = +5\;nC\]
Find the electric potential at a distance
\[r= 0.3\;m \]
Potential calculation (V):
\[V = (8.99×10^9) × \frac {5×10^{-9}}{0.3}\]
\[V = 149.83 V \]
Key Differences Between Potential and Field
- Field is a vector while potential is a scalar
- Field depends on inverse square of distance
\[\frac { 1}{r²}\]
while potential depends on inverse of distance
\[\frac {1}{r}\]
- Field relates to force, potential relates to energy
Uniform Electric Field and Potential
Uniform Electric Field
Uniform Electric Field
Definition:
A uniform electric field is a constant electric field in magnitude and direction between two parallel charged plates, calculated from surface charge density.
Mathematical Relation:
Field strength (E) = Surface charge density (σ) / Permittivity of free space (ε₀)
\[E = \frac {σ }{ ε₀}\]
Affecting Factors:
- Surface charge density (σ)
- Permittivity of the medium (ε)
- Applied potential between plates
Uniform Field Properties:
- Constant field strength in magnitude and direction
- Parallel and equally spaced field lines
- Constant force on a test charge
- Electric potential varies linearly with distance
Practical Example:
Question: Two parallel plates each with area
\[A=2\; m² \]
and charge
\[q=8.85 × 10^{-12}\; C\]
Calculate the electric field strength?
Solution:
- Calculate surface charge density (σ) = Charge / Area
- \[σ = \frac {8.85 × 10^{-12}}{ 2} = 4.425 × 10^{-12} C/m²\]
- \[E = \frac {σ }{ ε₀} =\frac {4.425 × 10^{-12}}{ 8.85 × 10^{-12}}\]
- \[E = 0.5 N/C\]
Uniform Electric Potential
Uniform Electric Potential
Scientific Concept:
Uniform electric potential occurs when the electric field is constant in magnitude and direction, resulting in linear variation of potential with distance.
Mathematical Relation:
\[ ΔV = -E × d × cosθ\]
Where:
- ΔV: Potential difference (Volt)
- E: Electric field strength (Volt/meter)
- d: Distance (meter)
- θ: Angle between field direction and motion direction
Affecting Factors:
- Electric field strength (E)
- Distance traveled (d)
- Direction of motion relative to field (θ)
Practical Example:
If a uniform electric field has strength
\[E=50 \;v/m\]
and a charge is moved 3 meters parallel to the field, the potential difference is
\[ ΔV = -(50) × 3 × cos(0°) = -150\; V\]
Key Properties:
- Linear variation of potential with distance
- Direction of steepest potential drop matches electric field direction
- Equipotential surfaces are parallel and equally spaced
- Electric field is negative spatial gradient of potential (E = -∇V)
Important Notes:
1. Negative sign indicates direction of potential decrease
2. Potential increases when moving against the field
3. No potential change when moving perpendicular to field (θ = 90°)
Electric Field and Potential Calculations
Electrical Calculations
1. Electric field of point charge
Result:
2. Electric field from surface charge
Result:
3. Electric potential of point charge
Result:
4. Potential between capacitor plates
Result:
Electric Field and Potential for Point Charges and Capacitor Plates |
Electric Field and Potential for Point Charges
Electric Field
Definition: The region of space around a charge where electric forces act on other charges.
Determining Direction
There are two methods to determine directionMethod 1: Place a test charge at the point where direction needs to be determined
According to vector rules, multiplying a number by a vector
If a positive test charge is placed, the field direction is the same as the force direction
If the test charge is negative, the field direction is opposite to the electric force direction Method 2: By drawing field lines for positive and negative charges
Field lines for positive charges radiate outward
Field lines for negative charges point inward
Electric Field Properties:
- Vector quantity (has magnitude and direction)
- Created by any electric charge
- Measured in N/C or V/m
- Scalar quantity (magnitude only)
- Depends on distance from the charge
- Measured in Volt (V)
- Field is a vector while potential is a scalar
- Field depends on inverse square of distance \[\frac { 1}{r²}\] while potential depends on inverse of distance \[\frac {1}{r}\]
- Field relates to force, potential relates to energy
- Surface charge density (σ)
- Permittivity of the medium (ε)
- Applied potential between plates
- Constant field strength in magnitude and direction
- Parallel and equally spaced field lines
- Constant force on a test charge
- Electric potential varies linearly with distance
- Calculate surface charge density (σ) = Charge / Area
- \[σ = \frac {8.85 × 10^{-12}}{ 2} = 4.425 × 10^{-12} C/m²\]
- \[E = \frac {σ }{ ε₀} =\frac {4.425 × 10^{-12}}{ 8.85 × 10^{-12}}\]
- \[E = 0.5 N/C\]
- Electric field strength (E)
- Distance traveled (d)
- Direction of motion relative to field (θ)
- Linear variation of potential with distance
- Direction of steepest potential drop matches electric field direction
- Equipotential surfaces are parallel and equally spaced
- Electric field is negative spatial gradient of potential (E = -∇V)
Practical Example:
Point charge \[ Q = +5\;nC\] Find the electric field at a distance \[r= 0.3\;m \]
Field calculation (E):
\[E = (8.99×10^9) × \frac {5×10^{-9}}{0.3^2}\]
\[E = 499.4 N/C\]
Electric Potential
Definition: The work needed to move a unit positive charge from infinity to the desired point.
Electric Potential Properties:
Practical Example:
Point charge \[ Q = +5\;nC\] Find the electric potential at a distance \[r= 0.3\;m \]
Potential calculation (V):
\[V = (8.99×10^9) × \frac {5×10^{-9}}{0.3}\]
\[V = 149.83 V \]
Key Differences Between Potential and Field
Uniform Electric Field and Potential
Uniform Electric Field
Definition:
A uniform electric field is a constant electric field in magnitude and direction between two parallel charged plates, calculated from surface charge density.
Mathematical Relation:
\[E = \frac {σ }{ ε₀}\]
Affecting Factors:
Uniform Field Properties:
Practical Example:
Question: Two parallel plates each with area \[A=2\; m² \] and charge \[q=8.85 × 10^{-12}\; C\] Calculate the electric field strength?
Solution:
Uniform Electric Potential
Scientific Concept:
Uniform electric potential occurs when the electric field is constant in magnitude and direction, resulting in linear variation of potential with distance.
Mathematical Relation:
\[ ΔV = -E × d × cosθ\]
Where:
- ΔV: Potential difference (Volt)
- E: Electric field strength (Volt/meter)
- d: Distance (meter)
- θ: Angle between field direction and motion direction
Affecting Factors:
Practical Example:
If a uniform electric field has strength
\[E=50 \;v/m\]
and a charge is moved 3 meters parallel to the field, the potential difference is
\[ ΔV = -(50) × 3 × cos(0°) = -150\; V\]
Key Properties:
Important Notes:
1. Negative sign indicates direction of potential decrease
2. Potential increases when moving against the field
3. No potential change when moving perpendicular to field (θ = 90°)
Electrical Calculations
1. Electric field of point charge
Result:
2. Electric field from surface charge
Result:
3. Electric potential of point charge
Result:
4. Potential between capacitor plates
Result:
0 Comments