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Coulomb's Law - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Coulomb's Law is considered one the most difficult concept.
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88 Questions around this concept.
Solve by difficulty
Two identical charged spheres suspended from a common point by two massless strings of length are initially a distance
apart because of their mutual repulsion. The charge begins to leak from both spheres at a constant rate. As a result, the charges approach each other with a velocity
. Then the relation between v and x is:
With the rise in temperature, the dielectric constant $K$ of a liquid
A force $F$ acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air. The permittivity of air and dielectric constant of water are $\varepsilon_0$ and $K$ respectively. When a piece of salt is put in water electrical force acting between sodium and chlorine ions 1 cm apart is
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A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then the Q/q equals
Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance.A third spherical conductor having same radius as that of B but uncharged is brought in contact with B then brought in contact with C and finally removed away from both, The new force of repulsion between B and C is :
Two charges equal in magnitude and opposite in polarity are placed at a certain distance apart and force acting between them is F. If 75% charge of one is transferred to another, then the force between the charges becomes
Two identical metallic spheres A and B when placed at a certain distance in the air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:
Two identical tennis balls each having mass ' $m$ ' and charge ${ }^{\prime} q^{\prime}$ are suspended from a fixed point by threads of length ' $l^{\prime}$ What is the equilibrium separation when each thread makes a small angle $\Theta^{\prime}$ with the vertical?
Two equal negative charge – q are fixed at the fixed points (0,a) and (0.-a) on the Y-axis. A positive charge Q is released from rest at the point (2a, 0) on the X-axis. The charge Q will
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Try NowTwo charges and
are placed in vacuum at a distance
and the force acting between them is
. If a medium of dielectric constant 4 is introduced around them, the force now will be:
Concepts Covered - 1
Coulomb's Law
Coulomb's Law: The force of attraction or repulsion between two charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.
$
\begin{aligned}
& F \propto \frac{Q_1 Q_2}{r^2} \\
& F=\frac{K Q_1 Q_2}{r^2}
\end{aligned}
$
$\mathrm{K}=$ Proportionality Constant
$Q_1$ and $Q_2$ are two Point charges
In SI unit value of K is
$
K=\frac{1}{4 \pi \varepsilon_0}
$
Where,
$
\left(\varepsilon_0\right)=8.85 \times 10^{-12} \frac{C^2}{N-m^2} \text { known as absolute permittivity of air or free }
$
space
The vector form of Coulomb's Law:
Consider two charges $q_1$ and $q_2$ separated by a distance r. Let the position vectors of $q_1$ be $r_1$ and that of $q_2$ be $r_2$. Then the force due to $q_2$ on $q_1$ as shown in figure $F_{12}$ is directed along the unit vector $r_{12}$ and
$
\begin{aligned}
& F_{12}=\frac{K q_1 q_2}{r^2} \hat{r}_{12} \\
& \text { here, } \hat{r}_{12}=\frac{\vec{r}_1-\vec{r}_2}{\left|r_1-r_2\right|}=\frac{\vec{r}_{12}}{r} \\
& F_{12}=\frac{K q_1 \cdot q_2}{r^3} \vec{r}_{12}
\end{aligned}
$
Force when dielectric inserted between the charges:
When a dielectric of dielectric constant $k$ is completely filled between the charges then force
$
F_{\text {med }}=\frac{q_1 q_2}{4 \pi \varepsilon_0 k r^2}=\frac{q_1 q_2}{4 \pi \varepsilon_0 \epsilon_r r^2}
$
$\epsilon_r$ is relative permittivity / dielectric constant of the medium. The dielectric constant is the ratio of the permittivity of a substance to the permittivity of free space. (dielectric will be explained later in detail in this chapter)
If the dielectric of thickness d is partially filled between the charges $Q_1$ and $Q_2$ then
$F=\frac{Q_1 Q_2}{4 \pi \epsilon_0(r-d+\sqrt{k} d)^2}$
Principle of Superposition:
It states that the total force acting on a given charge due to a number of charges is the Vector sum of the individual forces acting on that charge due to all the charges.
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