Electrostatics

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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a month 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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a month 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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a month 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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a month 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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a month 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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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 month ago

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:

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