The principle of superposition for electrostatic forces is a fundamental concept in electrostatics. It describes how to calculate the total force on a charge when multiple other charges are present. Forces are vector quantities, meaning they have both magnitude and direction.
Correct Option: C) Net force is the vector sum of individual forces
This statement accurately defines the principle of superposition for electrostatic forces. The net force on a charge due to multiple other charges is found by calculating the individual force exerted by each charge and then adding these forces vectorially.
The question asks about the meaning of the conservation of electric charge. This is a fundamental principle in physics, similar to the conservation of energy or momentum. Understanding this principle requires knowing what it implies about the total charge within a defined system.
D) Total charge in an isolated system is constant. This statement accurately defines the law of conservation of electric charge. It means that within a system that is closed off from its surroundings (isolated), the sum of all positive and negative charges will always remain the same, regardless of any interactions or transformations occurring within that system.
This problem involves Coulomb's Law, which describes the force between two electric charges. The force depends on the magnitude of the charges, the distance between them, and the medium in which they are placed. The dielectric constant (K) of the medium plays a crucial role in determining this force.
Coulomb's Law in a vacuum/air: The force \(F\) between two charges \(q_1\) and \(q_2\) separated by a distance \(r\) in a vacuum or air is given by:
\[ F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \]where \(\epsilon_0\) is the permittivity of free space.
Coulomb's Law in a medium: When the charges are immersed in a medium with a dielectric constant \(K\), the permittivity of the medium becomes \(\epsilon = K\epsilon_0\). The new force \(F'\) in the medium is:
\[ F' = \frac{1}{4\pi\epsilon} \frac{q_1 q_2}{r^2} = \frac{1}{4\pi K\epsilon_0} \frac{q_1 q_2}{r^2} \]Relating F and F': We can express \(F'\) in terms of \(F\):
\[ F' = \frac{1}{K} \left( \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2} \right) \]Since \[F = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}\], we have:
\[ F' = \frac{F}{K} \]Substitute the given value: The dielectric constant of water is given as \(K = 80\). Substituting this value into the equation:
\[ F' = \frac{F}{80} \]Therefore, the new force when the charges are immersed in water is \(F/80\).
Correct Option: A) F/80 is the correct answer because the force between two charges decreases by a factor equal to the dielectric constant of the medium when they are immersed in it.
The question asks for the definition of electric field intensity (E) at a point. We need to recall the fundamental definition of electric field intensity in physics.
B) Force per unit positive test charge. This is the standard definition of electric field intensity. It quantifies the strength of the electric field at a point by measuring the force exerted on a very small positive test charge placed at that point, divided by the magnitude of that test charge.
The electric field intensity, also known as the electric field strength, is defined as the force experienced per unit positive test charge. We can derive its SI unit from this definition and also from its relationship with electric potential.
Correct Option: D) N/C or V/m — This option correctly lists both common and equivalent SI units for electric field intensity, derived from its definition as force per unit charge and its relation to electric potential gradient.
The question asks for the formula for the electric field due to a point charge. This is a fundamental concept in electrostatics, derived from Coulomb's Law.
Correct Option: C) The electric field due to a point charge \(q\) at a distance \(r\) is given by the formula \(E = \frac{kq}{r^2}\). This formula correctly represents the inverse square relationship with distance and direct proportionality to the charge magnitude.