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Physics · Electrostatic Potential
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Physics · Electrostatic Potential
Two point charges \( 3 \times 10^{-8}\text{ C} \) and \( -2 \times 10^{-8}\text{ C} \) are placed \( 15\text{ cm} \) apart. The electric potential is zero at a point on the line joining the two charges, at a distance from the positive charge given by:
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Given below are two statements: Statement I: The capacitance of a parallel plate capacitor depends solely on the geometrical configuration (shape, size, separation of the plates) and the medium between the plates. Statement II: Capacitance increases linearly with the amount of charge \( Q \) supplied to the plates. In the light of the above statements, choose the most appropriate answer from the options given below:
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Consider the following statements about a parallel plate capacitor with plate area \( A \) and separation \( d \) filled with vacuum: (I) The electric field just outside the plates (in Region I and II) is zero. (II) The electric field inside the plates is given by \( E = \frac{Q}{\varepsilon_0 A} \). (III) The potential difference between the plates is \( V = E d \). (IV) The capacitance \( C \) decreases if the separation \( d \) is decreased. Which of the above statements are correct?
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Given below are two statements: Statement I: The potential at the center of a hollow conducting sphere having surface charge density \( \sigma \) and radius \( R \) is zero. Statement II: The electric field at the center of a hollow conducting sphere of radius \( R \) carrying surface charge density \( \sigma \) is zero. In the light of the above statements, choose the most appropriate answer from the options given below:
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Given below are two statements: Statement I: The potential due to a dipole at any point depends on the position vector magnitude \( r \) and the angle \( \theta \) between \( \mathbf{r} \) and dipole moment \( \mathbf{p} \). Statement II: The electric field of a dipole at a point depends only on the magnitude \( r \) and is independent of angle \( \theta \). In the light of the above statements, choose the most appropriate answer from the options given below:
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Based on the arrangement shown in Figure 2.1, when a test charge \( q \) is moved from \( R \) to \( P \) against a repulsive force, what does the integration \( W_{RP} = -\int_R^P \mathbf{F}_{\text{ext}} \cdot d\mathbf{r} \) physically represent?
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An electric dipole of dipole moment \( p \) is placed in a uniform electric field \( \mathbf{E} \). If the dipole is rotated from an angle \( \theta = 0^\circ \) to \( \theta = 180^\circ \), the work done by the external agent is:
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Two point charges \( q_1 \) and \( q_2 \) are placed at a distance \( r \) apart. The electric potential energy of the system is given by:
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The electrostatic potential energy difference between two points \( R \) and \( P \) in an electric field is given by \( \Delta U = U_P - U_R = W_{RP} \). What is the physical significance of this quantity?
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Which of the following physical quantities is a scalar and represents the potential energy per unit positive test charge in an electric field?
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Given below are two statements: Statement I: The extent of polarisation in a polar dielectric decreases as the temperature of the dielectric is lowered. Statement II: Thermal energy tends to align the molecular dipoles parallel to the external electric field. In the light of the above statements, choose the most appropriate answer from the options given below:
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The relation between electric field \( \mathbf{E} \) and electric potential \( V \) across closely spaced equipotential surfaces is given by \( |\mathbf{E}| = -\frac{\delta V}{\delta l} \). The negative sign indicates that:
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The electric potential at a point on the axial line of an electric dipole of dipole moment \( p \) at a distance \( r \) (where \( r \gg a \)) is given by \( V = \pm \frac{1}{4\pi\varepsilon_0} \frac{p}{r^2} \). If the distance \( r \) is doubled, the potential at the axial point becomes:
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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 equivalent capacitance of a parallel combination of capacitors is always less than the capacitance of the smallest individual capacitor in the combination. Reason (R): In a parallel combination of capacitors, the total charge is distributed among the capacitors in proportion to their individual capacitances. In the light of the above statements, choose the correct answer from the options given below:
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A test charge \( q \) is moved slowly from a point \( R \) to a point \( P \) against a repulsive electrostatic force due to a source charge \( Q \) placed at the origin. Which of the following statements regarding the work done by the external force \( F_{\text{ext}} \) is correct?
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Consider the following statements regarding electrostatic potential: (I) Potential at a point due to a point charge \( Q \) is inversely proportional to distance \( r \). (II) For a negative charge, potential is negative. (III) Electrostatic potential is a vector quantity. (IV) The unit of electrostatic potential is joule per coulomb. How many of the above statements are correct?
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Which of the following expressions correctly represents the SI unit of capacitance, 1 Farad (\( 1\text{ F} \))?
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Consider the following statements regarding the molecular properties of dielectrics: (A) In \( \(\text{CO}\)_2 \), the individual \( \(\text{C}\)-\(\text{O}\) \) bond dipoles cancel each other due to its linear shape. (B) Water (\( \(\text{H}\)_2\(\text{O}\) \)) molecule has a permanent dipole moment because of its bent structure. (C) In a uniform electric field, the alignment of polar molecules is completely rigid and independent of thermal motion. (D) For linear isotropic dielectrics, the induced dipole moment is directly proportional to the applied electric field. Which 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): When a dielectric medium is completely placed between the plates of a charged capacitor, the capacitance always increases by a factor \( K > 1 \). Reason (R): Polarization of the dielectric produces bound charges of opposite sign near the plates, which decreases the net electric field inside the dielectric for a given free charge on the plates. 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 work done in bringing a test charge \( q \) from infinity to a point inside an external field is independent of the path taken. Reason (R): The electrostatic field is a conservative force field. In the light of the above statements, choose the correct answer from the options given below:
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A parallel plate capacitor is charged by a DC battery and remains continuously connected to it. A dielectric slab of dielectric constant \( K > 1 \) is now slowly inserted into the space between the plates. Consider the following statements: (A) The potential difference between the plates remains constant. (B) The electric field between the plates decreases by a factor of \( K \). (C) The capacitance of the capacitor increases by a factor of \( K \). (D) The electrostatic energy stored in the capacitor increases by a factor of \( K \). Which of the above statements are correct?
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In a parallel-plate capacitor, the electric field between plates is \( E_0 \). If a conducting slab of thickness \( t = \frac{d}{2} \) (where \( d \) is plate separation) is inserted between the plates without touching them, the ratio of new capacitance to initial capacitance is:
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