Conductors & Electrostatic Properties questions with solutions

Showing 1–10 of 63 questions

• MCQmediumElectrostaticConductors & Electrostatic Properties

  Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\vec{p}$ as shown. In this case

  

  Options

  • Option A

    Electric field outside the shell is the same as that of a point charge Q at the centre.

  • Option B

    Surface charge density on the inner surface is zero everywhere.

  • Option C

    Surface charge density on the inner surface is uniform and equal to $\frac{\frac{Q}{2}}{4\pi a^2}$

  • Option D

    Surface charge density on the outer surface depends on $\left\vert\vec{p}\right\vert$

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  JEE Mains 2019

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• Multi-correctmediumElectrostaticConductors & Electrostatic Properties

  As shown in figure a point charge 1q is placed inside a neutral conducting shell at a distance R/2 from the centre of shell. Another point charge 2q is placed at a distance $\frac{\sqrt7}{2}$R from the centre of shell. Choose the correct option(s).

  

  Select all that apply

  • Option A

    The magnitude of force on q₁ due to induced charges at the inner surface of the conducting shell is zero.

  • Option B

    The magnitude of force on q₁ due to induced charges at the outer surface of the conducting shell is q₁q₂/8πε₀R²

  • Option C

    The magnitude of force on q₂ due to induced charges at the inner surface of the shell is zero.

  • Option D

    The magnitude of force on q₂ due to induced charges at the inner surface of the shell is q₁q₂ /8πε₀R²

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• MCQmediumElectrostaticConductors & Electrostatic Properties

  An ellipsoidal cavity is carved within a perfect conductor. A positive charge q is placed at the center of the cavity. The points A & B are on the cavity surface as shown in the figure. Then :

  

  Options

  • Option A

    electric field near A in the cavity = electric field near B in the cavity

  • Option B

    charge density at A = charge density at B

  • Option C

    potential at A = potential at B

  • Option D

    total electric field flux through the surface of the cavity is q/ε₀.

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• MCQmediumElectrostaticConductors & Electrostatic Properties

  An isolated conducting sheet of area A and carrying a charge Q is placed in a uniform electric field E, such that electric field is perpendicular to sheet and covers all the sheet. Find out charges appearing on right surface of plate.

  

  Options

  • Option A

    $\frac{Q}{2}-EA\varepsilon_{\omicron}$

  • Option B

    $\frac{Q}{2}-2EA\varepsilon_{\omicron}$

  • Option C

    $\frac{Q}{2}+EA\varepsilon_{\omicron}$

  • Option D

    $\frac{Q}{2}+2EA\varepsilon_{\omicron}$

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• Multi-correctdifficultElectrostaticConductors & Electrostatic Properties

  A small neutral metal sphere is placed between the plates of an ideal parallel-plate capacitor. After electrostatic equilibrium is established, which statements are correct?

  

  Select all that apply

  • Option A

    The sphere is polarized

  • Option B

    The electric field inside the metal is zero

  • Option C

    Electric field lines meet the sphere surface normally

  • Option D

    The sphere acquires a nonzero net charge

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• IntegermediumElectrostaticConductors & Electrostatic Properties

  Three concentric spherical metallic shells X, Y and Z of radii a, b and c (a < b < c) have surface charge densities +σ, -σ and +σ respectively. Shells X and Z are at the same potential. If a = 2 cm and b = 3 cm, find c in cm.

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  JEE Mains10 April 2023Shift 1Morning Shift

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• MCQmediumElectrostaticConductors & Electrostatic Properties

  The electric field in a region is 𝐄 = 3y $\hat{j}.$ Find the total electrostatic energy stored in the electric field inside the cube of side a shown in the figure.

  

  Options

  • Option A

    9ε₀a⁵

  • Option B

    3ε₀a⁵

  • Option C

    (3/2)ε₀a⁵

  • Option D

    0

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• MCQmediumElectrostaticConductors & Electrostatic Properties

  A metal sphere A of radius r₁ charged to a potential f₁ is enveloped by a thin walled conducting spherical shell B of radius r₂. Then f₂ of the sphere A after it is connected by a thin wire to the shell B will be :-

  

  Options

  • Option A

    $f_1$$\frac{r_1}{r_2}$

  • Option B

    $f_1\left(\frac{r_2}{r_1}\right)$

  • Option C

    $f_1\left(1-\frac{r_1}{r_2}\right)$

  • Option D

    $f_1\left(\frac{r_1r_2}{r_1+r_{^2}}\right)$

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• MCQmediumElectrostaticConductors & Electrostatic Properties

  Two isolated conducting spheres S₁ and S₂ have radii r₁ = 2R/3 and r₂ = R/3. They initially carry charges q₁ = +12 μC and q₂ = -3 μC, respectively, and are very far apart. They are connected by a conducting wire. After electrostatic equilibrium is reached, the charges on S₁ and S₂ are:

  Options

  • Option A

    6 μC and 3 μC

  • Option B

    +4.5 μC and -4.5 μC

  • Option C

    3 μC and 6 μC

  • Option D

    4.5 μC on both

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• Multi-correctmediumElectrostaticConductors & Electrostatic Properties

  For the situation shown in the figure below, mark out the correct statement(s)

  

  Select all that apply

  • Option A

    Potential of the conductor is q/4πε₀(d+R)

  • Option B

    Potential of the conductor is q/4πε₀d

  • Option C

    Potential of the conductor can’t be determined as nature of distribution of induced charges is not known

  • Option D

    Potential at point B due to induced charges is -qR/4πε₀(d+R)d

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