Electric potential and capacitance practice · Mixed difficulty

Option A is correct because the dielectric constant generally increases from air to rubber to copper due to increasing polarization and conductivity.

Option B ($\frac{1}{{4\pi { \in _\mathrm{o}}}}\frac{q}{r}$) is correct because the potential at any point on a conducting sphere is constant and equal to the potential at the surface due to the external charge.

The correct answer is C ($18 \times {10^{ - 26}}$ Nm) because the maximum torque on a dipole in an electric field is given by $\tau = pE$.

Option C ($\frac{1}{d^3}$) is correct because the electric field due to an electric dipole at a point on its axis is inversely proportional to the cube of the distance from the center of the dipole.

Option C (Potentiometer does not draw any current from the unknown source of emf to be measured) is correct because a potentiometer works on the null deflection method, drawing no current from the source being measured, thus providing a more accurate potential difference reading.

Option A (Their capacities are equal) is correct because the parallel combination being four times the series combination implies equal capacitances.

Option A (Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1) is correct because the earth is taken as zero potential and the potential of a sphere is given by the formula in statement 2.

Option C (-30 J) is correct because it calculates the potential energy of the dipole using the formula $U = -pE \cos \theta$ after finding the dipole moment $p$ from the torque equation.

Option D (Information is not enough to give answer) is correct because conductors are equipotential, meaning the potential is the same everywhere on the conductor.

Option C (The field between the plates) is correct because the energy stored in a capacitor is stored in the electric field created between its plates.

Option D ($k.\frac{{\vec p.\vec r}}{{{{r^3}}}}$) is correct because it represents the electric potential due to a dipole at a given point in space.

Option A (4 esu) is correct because it is the charge on the first sphere after they are connected.

Option A is correct because conductors with the same charge can have different potentials due to different capacitances, which depend on size.

Option A (If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion) is correct because a positive charge moves from higher to lower potential due to the electric field.

Option C (15 micro farad) is correct because the charge is conserved when the capacitors are connected, allowing us to calculate the capacitance of the second capacitor.

Option A (Scalar and vector) is correct because potential is a scalar quantity, while the potential gradient is a vector quantity.

Option C (CE) is correct because after connecting to the emf source, the capacitor will charge to a voltage E, resulting in a charge of CE.

Option C is correct. The net electrostatic force on -Q is zero due to symmetry, but the net electrostatic potential at the center is not zero because potential is a scalar quantity.

Option B (Increases) is correct because adding charge to a soap bubble increases its potential energy, leading to an increase in radius to minimize the energy.

Option D ($\frac{1}{2} \varepsilon_0\left(\frac{\mathrm{V}^2}{\mathrm{d}^2}\right)$) is correct because it represents the energy density in terms of permittivity and electric field.

Option D is correct because when a battery supplies power, the electrostatic force does negative work on positive charges moving from the negative to the positive terminal, and the electric field inside a battery is directed from the positive to the negative electrode.

Option B (Increase) is correct because moving a positive charge to a higher potential increases its potential energy.

Option C (Inversely proportional to the distance) is correct because the electric potential due to a point charge decreases as the distance from the charge increases.

Option B ($4\mathrm{ }:\mathrm{ }1$) is correct because it correctly calculates the ratio of potentials using the relationship between potential and radius for charged spheres.

Option C (Decreases because the charge moves along the electric field) is correct because a positive charge moves in the direction of the electric field, decreasing its potential energy.

Option D (Assertion is false and Reason is true) is correct because positive charge flows from higher potential to lower potential, meaning from the smaller sphere to the bigger sphere if they have the same initial charges, and electrostatic potential energy is indeed lost during charge redistribution.

Option D is correct because when the dielectric is pulled out after disconnecting the battery, the charge remains constant, the capacitance decreases, and thus the energy stored in the capacitor increases.

Option C ($- \frac{{dV}}{{dx}}$) is correct because the electric field is the negative gradient of the electric potential.

Option C ($1.8 \times 10^{-29} \mathrm{~Cm}$) is correct because it is the calculated dipole moment using the given torque, electric field, and angle.

Option A is correct because the electric field is the negative gradient of the electric potential, and if the potential is constant, its gradient is zero.