Electrostatics

Three capacitors each of capacitance C = 2μF are connected with a battery of emf 30V as shown in the figure. When the switch S is closed, the heat generated in circuit will be n/10 mJ. Find the value of n.

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Ui = ½C (V/3)² + ½C (V/3)² + ½C (2V/3)²
Uf = ½CV²
Wb = CV²/3
ΔH = [Wb - (Uf - Ui)] = CV²/6 = 0.30 mJ

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2 months ago

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

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(4/3)πR³ = 27 (4/3)πr³) ⇒ R = 3r (i)
v = Kq/r = V? /r = (q? /q? ) (r? /r? ) (i)
⇒ 220/V? = (q/ (27q) (3r/r) (i)
⇒ 220/V? = 1/9 (i)
⇒ V? = 220 * 9 = 1980 volt (i)

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2 months ago

The equivalent capacitance of the combination shown in the figure is:

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A dipole is placed in an electric field ns shown. In which direction will it move?

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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:

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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?

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2 months ago

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]

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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

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2 months ago

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.

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The flux φ is calculated as:
φ = (2/5) * 4 * 10³ * 0.4 = 640 Nm²C? ¹

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2 months ago

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)

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Kindly consider the following figure

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2 months ago

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)

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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) = CV²/ (2k)

U_f = (14 * 10? ¹² * 12²) / (2 * 7) = 144 pJ

Mechanical energy available for oscillation

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2 months ago

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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