Electrostatics
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The equivalent capacitance of the combination shown in the figure is:
The equivalent capacitance of the combination shown in the figure is:
A dipole is placed in an electric field ns shown. In which direction will it move?
A dipole is placed in an electric field ns shown. In which direction will it move?
Two charged spherical conductors of radius R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres (σ₁/σ₂) is:
Two charged spherical conductors of radius R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres (σ₁/σ₂) is:
For a conducting sphere, the electric field E = σ/ε? and potential V = σR/ε?
When two spheres are connected by a wire, their potentials become equal: V? = V?
σ? R? /ε? = σ? R? /ε?
σ? R? = σ? R? ⇒ σ? /σ? = R? /R?
Upvote 
An infinite number of point charges, each carrying 1 μC charge, are placed along y-axis at y = 1 m, 2 m, 4 m, 8 m, . The total force on a 1 C point charge, placed at the origin is x×103 N. The value of x, to the nearest integer, is.
[Take 1/(4πε?) = 9×109 Nm2/C2]
An infinite number of point charges, each carrying 1 μC charge, are placed along y-axis at y = 1 m, 2 m, 4 m, 8 m, . The total force on a 1 C point charge, placed at the origin is x×103 N. The value of x, to the nearest integer, is.
[Take 1/(4πε?) = 9×109 Nm2/C2]
F = (qQ)/ (4πε? r? ²) + (qQ)/ (4πε? r? ²) + (qQ)/ (4πε? r? ²) + (qQ)/ (4πε? r? ²) + .
⇒ F = (qQ)/ (4πε? ) [1/1² + 1/2² + 1/4² + 1/8² + .]
⇒ F = (qQ)/ (4πε? ) [1/ (1 - 1/4)]
⇒ F = (qQ)/ (4πε? ) [4/3] = 10? × 1 × 9 × 10? × (4/3) = 12 × 10³ N
Upvote The electric field in a region is given by E⃗ = (2/5)E₀ î + (3/5)E₀ ĵ with E₀ = 4.0 × 10³ N/C. The flux of this field through a rectangular surface area 0.4m² parallel to the Y-Z plane is _____ Nm²C⁻¹.
The electric field in a region is given by E⃗ = (2/5)E₀ î + (3/5)E₀ ĵ with E₀ = 4.0 × 10³ N/C. The flux of this field through a rectangular surface area 0.4m² parallel to the Y-Z plane is _____ Nm²C⁻¹.
The flux φ is calculated as:
φ = (2/5) * 4 * 10³ * 0.4 = 640 Nm²C? ¹
Upvote Four identical rectangular plates with length, l = 2cm and breadth, b = 3/2 cm are arranged as shown in figure. The equivalent capacitance between A and C is xε0A/d. The value of x is ----------. (Round off to the nearest integer)
Four identical rectangular plates with length, l = 2cm and breadth, b = 3/2 cm are arranged as shown in figure. The equivalent capacitance between A and C is xε0A/d. The value of x is ----------. (Round off to the nearest integer)
Kindly consider the following figure
Upvote A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12V between its plates. The charging battery is now disconnected and a porcelain plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of . pJ. (Assume no friction)
A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12V between its plates. The charging battery is now disconnected and a porcelain plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of . pJ. (Assume no friction)
Initial charge Q = CV = 14 × 10? ¹² × 12 = 168 × 10? ¹² C
Initial energy U_in = ½ CV² = ½ (14 × 10? ¹²) × 12² = 1008 pJ
When the battery is disconnected and a dielectric (k=7) is inserted, the new capacitance is C' = kC.
The charge Q remains constant.
Final energy U_f = Q²/2C' = Q²/ (2kC) = (CV)²/ (2kC)
Upvote Two capacitors of capacitances C and 2C are charged to potential differences V and 2 V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:
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Two capacitors of capacitances C and 2C are charged to potential differences V and 2 V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:
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A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height h (see figure), then: (assume the remaining portion to be spherical)
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A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height h (see figure), then: (assume the remaining portion to be spherical)
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A capacitor C is fully charged with voltage V?. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C/2. The energy loss in the process after the charge is distributed between the two capacitor is:
A capacitor C is fully charged with voltage V?. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance C/2. The energy loss in the process after the charge is distributed between the two capacitor is:
Q? = CV?
U? = ½CV? ²
q? = (q? C)/ (C + C/2) = 2q? /3
q? = (q? (C/2)/ (C + C/2) = q? /3; Uf = q? ²/2C + q? ²/2 (C/2)
= (4q? ²/9x2C) + (q? ²/9C)
= (6q? ²/18C) = q? ²/3C = CV? ²/3
Energy loss in the process = U? – Uf
= ½CV? ² - CV? ²/3
= CV? ²/6
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