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Physics · Electrostatic Potential
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Physics · Electrostatic Potential
Consider the following properties of equipotential surfaces: (A) Equipotential surfaces are concentric spheres for a point charge. (B) Two equipotential surfaces can intersect. (C) Electric field is perpendicular to the equipotential surface. (D) Work done to move a charge on an equipotential surface is zero. How many of the above statements are correct?
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The electric field is always normal to the equipotential surface at every point. Reason (R): If the electric field had a non-zero component along the equipotential surface, work would be done in moving a charge along the surface. In the light of the above statements, choose the correct answer from the options given below:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When a dielectric slab is placed in an external electric field, the opposing field generated by induced charges completely cancels out the external field inside the dielectric. Reason (R): Dielectric materials have no (or a negligible number of) free charge carriers to facilitate complete charge neutralization. In the light of the above statements, choose the correct answer from the options given below:
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Under electrostatic equilibrium, the tangential component of the electric field at the surface of a charged conductor is:
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Match List-I with List-II: List-I List-II A Potential due to point charge I \( \propto \frac{1}{r^2} \) B Potential due to electric dipole II \( \propto \frac{1}{r} \) C Electric field due to point charge III Zero D Potential at equatorial point of dipole IV \( \propto \frac{1}{r^2} \) Choose the correct answer from the options given below:
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Consider the following statements regarding conductors in electrostatic equilibrium: (A) The electric field is zero everywhere inside the bulk of a conductor. (B) The electrostatic field at the surface of a charged conductor is tangential to the surface. (C) The entire volume of a conductor is an equipotential region. (D) Any excess static charge resides entirely on the outer boundary surface. Which of the above statements are correct?
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Given below are two statements: Statement I: In a non-polar molecule, the centres of positive and negative charges coincide, resulting in zero intrinsic dipole moment. Statement II: In a polar molecule, the centres of positive and negative charges are separated even when no external electric field is applied. In the light of the above statements, choose the most appropriate answer from the options given below:
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Two point charges \( q_1 = 7\ \mu\text{C} \) and \( q_2 = -2\ \mu\text{C} \) are placed at \( (-9\text{ cm}, 0, 0) \) and \( (9\text{ cm}, 0, 0) \) respectively in an external electric field \( E = A/r^2 \), where \( A = 9 \times 10^5\ \text{N}\cdot\text{m}^2/\text{C} \). What is the total electrostatic energy of the configuration?
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Two large, flat conducting plates carry uniform surface charge densities \( +\sigma \) and \( -\sigma \). What are the values of the electric field in the outer region (above the positively charged plate) and in the inner region between the plates?
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What is the potential energy of a charge of \( 2\text{ \mu C} \) brought from infinity to a point where the electrostatic potential is \( 5\times 10^4\text{ V} \)?
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A hollow conducting spherical shell of radius \( R \) has a total charge \( q \) distributed uniformly on its surface. The electric potential at a distance \( r \) from the centre, where \( r < R \), is:
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An electric dipole of moment \( \mathbf{p} \) is aligned at an angle \( \theta \) with a uniform electric field \( \mathbf{E} \). The work done by an external agent in turning the dipole from \( \theta_0 \) to \( \theta \) at infinitesimal angular speed is:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In a polar substance, in the absence of an external electric field, the material exhibits zero net dipole moment. Reason (R): A non-polar molecule develops an induced dipole moment only when placed in an external electric field. In the light of the above statements, choose the correct answer from the options given below:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The capacitance of a conductor depends directly on the magnitude of charge placed on it. Reason (R): For an isolated conductor, the ratio of its charge \( Q \) to its electric potential \( V \) is a constant determined solely by its geometry. In the light of the above statements, choose the correct answer from the options given below:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): In a series combination of unequal capacitors connected across a DC voltage source, the potential difference across the smallest capacitor is the maximum. Reason (R): In a series combination of capacitors, each capacitor carries the same charge \( Q \). In the light of the above statements, choose the correct answer from the options given below:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): No work is done in moving a test charge from one point to another on an equipotential surface. Reason (R): Electric field lines are perpendicular to equipotential surfaces. In the light of the above statements, choose the correct answer from the options given below:
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A parallel plate capacitor with plate area \( A \) and plate separation \( d \) is filled with a dielectric slab of dielectric constant \( K = 4 \) and thickness \( t = \frac{2}{3}d \). If the original capacitance without dielectric is \( C_0 \), what is the new capacitance of the system?
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A charge \( q \) is moved along a closed loop in the presence of an electrostatic field produced by a static charge configuration. The total work done by the electrostatic field in this closed path is:
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Given below are two statements: Statement I: A uniformly polarised dielectric slab has no net charge within its interior, but possesses non-zero induced surface charge densities on its faces perpendicular to the field. Statement II: The surface charges appearing on a polarised dielectric are free charges that can easily conduct electricity. In the light of the above statements, choose the most appropriate answer from the options given below:
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A parallel plate capacitor with vacuum between its plates has a plate separation of \( 0.885\text{ mm} \). What plate area \( A \) is required to produce a capacitance of \( 2\text{ nF} \)? (Take \( \varepsilon_0 = 8.85 \times 10^{-12}\text{ C}^2\cdot\text{N}^{-1}\cdot\text{m}^{-2} \))
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Consider the following statements about an electric dipole placed in a uniform electric field \( \mathbf{E} \): (A) The net force acting on the dipole is zero. (B) The net torque acting on the dipole is maximum when its dipole moment is parallel to \( \mathbf{E} \). (C) The potential energy is zero when the dipole moment is perpendicular to \( \mathbf{E} \) (taking potential energy to be zero at \( \(\theta\) = \(\pi\)/2 \)). (D) The potential energy is maximum when the dipole moment is antiparallel to \( \mathbf{E} \). Choose the correct answer from the options given below:
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Work done by an external force in bringing a test charge from infinity to a point in an electric field is path-independent. Reason (R): Electrostatic force is conservative, hence the line integral of electric field around any closed path is zero. In the light of the above statements, choose the correct answer from the options given below:
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