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Questions and Answers
If the distance between parallel plates is significantly smaller than the length of the plates, the non-uniformity of the electric field at the boundaries is considered irrelevant.
If the distance between parallel plates is significantly smaller than the length of the plates, the non-uniformity of the electric field at the boundaries is considered irrelevant.
True (A)
When a conductor is charged, its capacitance decreases linearly with the increase in potential.
When a conductor is charged, its capacitance decreases linearly with the increase in potential.
False (B)
Capacitance is a vector quantity, characterized by both magnitude and direction.
Capacitance is a vector quantity, characterized by both magnitude and direction.
False (B)
If two initially charged parallel plates are brought into contact, the resulting total charge is doubled and the electrical potential becomes zero.
If two initially charged parallel plates are brought into contact, the resulting total charge is doubled and the electrical potential becomes zero.
The SI unit of capacitance is the 'farad', which can also be expressed in base units as $M^{-1}L^{-2}T^{4}A^{2}$.
The SI unit of capacitance is the 'farad', which can also be expressed in base units as $M^{-1}L^{-2}T^{4}A^{2}$.
A spherical conductor in a medium with permitivity $\epsilon_r$ has a capacitance of $C_{medium} = 4 \pi \epsilon_0 R \epsilon_r$, where R is the radius of the sphere.
A spherical conductor in a medium with permitivity $\epsilon_r$ has a capacitance of $C_{medium} = 4 \pi \epsilon_0 R \epsilon_r$, where R is the radius of the sphere.
Decreasing the overlapping area between the plates of a parallel plate capacitor will lead to an increase in the capacitor's overall capacitance.
Decreasing the overlapping area between the plates of a parallel plate capacitor will lead to an increase in the capacitor's overall capacitance.
The edges of a parallel plate capacitor exhibit a completely uniform electric field, identical to the field in the center of the capacitor.
The edges of a parallel plate capacitor exhibit a completely uniform electric field, identical to the field in the center of the capacitor.
If the charge on an isolated spherical conductor doubles, its capacitance quadruples.
If the charge on an isolated spherical conductor doubles, its capacitance quadruples.
The potential, $V$, of an isolated spherical conductor with charge $Q$ is given by $V = \frac{1}{2 \pi \epsilon_0 R}Q$
The potential, $V$, of an isolated spherical conductor with charge $Q$ is given by $V = \frac{1}{2 \pi \epsilon_0 R}Q$
Flashcards
Capacitance (C)
Capacitance (C)
The ability of a conductor to store electric charge, defined as the ratio of charge to potential.
Parallel Plate Capacitor
Parallel Plate Capacitor
A capacitor formed by two parallel conducting plates separated by a small distance.
Effect of Sliding Plates
Effect of Sliding Plates
The capacitance decreases as the overlapping area of the plates decreases.
Edge Effect in Capacitors
Edge Effect in Capacitors
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Spherical Conductor Potential
Spherical Conductor Potential
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Capacitor in a Medium
Capacitor in a Medium
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Study Notes
Vecteurs: Définitions
- A scalar is a numerical quantity fully defined by its magnitude on a scale
- A vector is a quantity defined by both magnitude and direction
- Vector notation can be: $\vec{A}$ or $\overrightarrow{AB}$
- The magnitude of a vector is represented by: $|\vec{A}|$ or $A$
Vecteurs: Opérations
Addition
- Triangle rule: $\vec{A} + \vec{B} = \vec{C}$
- Parallelogram rule: $\vec{A} + \vec{B} = \vec{C}$
- Vector addition is commutative: $\vec{A} + \vec{B} = \vec{B} + \vec{A}$
- Vector addition is associative: $\vec{A} + (\vec{B} + \vec{C}) = (\vec{A} + \vec{B}) + \vec{C}$
Soustraction
- Vector subtraction is defined by: $\vec{A} - \vec{B} = \vec{A} + (-\vec{B})$
Multiplication
- Scalar multiplication: $k\vec{A} = \vec{B}$
- $k(\vec{A} + \vec{B}) = k\vec{A} + k\vec{B}$
- $(k_1 + k_2)\vec{A} = k_1\vec{A} + k_2\vec{A}$
- $k_1(k_2\vec{A}) = (k_1k_2)\vec{A}$
Vecteurs: Unitaires et Composantes
- Cartesian unit vectors: $\hat{i} = (1, 0, 0)$, $\hat{j} = (0, 1, 0)$, $\hat{k} = (0, 0, 1)$
Composantes
- Vector $\vec{A}$ can be expressed as: $\vec{A} = A_x\hat{i} + A_y\hat{j} + A_z\hat{k}$
- Magnitude $A$ of vector $\vec{A}$: $A = |\vec{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2}$
Addition
- Addition in components: $\vec{A} + \vec{B} = (A_x + B_x)\hat{i} + (A_y + B_y)\hat{j} + (A_z + B_z)\hat{k}$
Produit Scalaire (Dot Product)
- $\vec{A} \cdot \vec{B} = |\vec{A}||\vec{B}|\cos\theta = A_xB_x + A_yB_y + A_zB_z$
Propriétés
- Commutative: $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$
- Distributive: $\vec{A} \cdot (\vec{B} + \vec{C}) = \vec{A} \cdot \vec{B} + \vec{A} \cdot \vec{C}$
- If $\vec{A} \cdot \vec{B} = 0$, then $\vec{A} \perp \vec{B}$ (given $\vec{A}, \vec{B} \neq 0$)
Produit Vectoriel (Cross Product)
- $\vec{A} \times \vec{B} = |\vec{A}||\vec{B}|\sin\theta \hat{n}$
- Where $\hat{n}$ is a unit vector perpendicular to the plane containing $\vec{A}$ and $\vec{B}$, determined by the right-hand rule
- $\vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ A_x & A_y & A_z \ B_x & B_y & B_z \end{vmatrix} = (A_yB_z - A_zB_y)\hat{i} - (A_xB_z - A_zB_x)\hat{j} + (A_xB_y - A_yB_x)\hat{k}$
Propriétés
- Anti-commutative: $\vec{A} \times \vec{B} = -\vec{B} \times \vec{A}$
- Distributive: $\vec{A} \times (\vec{B} + \vec{C}) = \vec{A} \times \vec{B} + \vec{A} \times \vec{C}$
- If $\vec{A} \times \vec{B} = 0$, then $\vec{A} \parallel \vec{B}$ (given $\vec{A}, \vec{B} \neq 0$)
Produit Mixte (Triple Scalar Product)
-
$\vec{A} \cdot (\vec{B} \times \vec{C}) = \begin{vmatrix} A_x & A_y & A_z \ B_x & B_y & B_z \ C_x & C_y & C_z \end{vmatrix}$
-
Geometrically this represents the volume of the parallelepiped formed by $\vec{A}, \vec{B}, \vec{C}$
Propriétés
- $\vec{A} \cdot (\vec{B} \times \vec{C}) = \vec{B} \cdot (\vec{C} \times \vec{A}) = \vec{C} \cdot (\vec{A} \times \vec{B})$
- $\vec{A} \cdot (\vec{B} \times \vec{C}) = - \vec{A} \cdot (\vec{C} \times \vec{B})$
Applications
- Calculating the area of a parallelogram/triangle
- Calculating the volume of a parallelepiped/tetrahedron
- Determining orthogonality/parallelism of vectors
- Calculating moments of forces
- Physics: work, flux, etc.
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