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Coulomb's Law - Practice Questions & MCQ

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

  • Coulomb's Law is considered one the most difficult concept.

  • 47 Questions around this concept.

Solve by difficulty

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d< < l) 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 \upsilon. Then the relation between v and x is:

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  :

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.

                                                                          \\F\propto \frac{Q_{1}Q_{2}}{r^{2}} \\ \\ \\F=\frac{KQ_{1}Q_{2}}{r^{2}}

 

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}}  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 figureF_{12} is directed along the unit vector r_{12} and

                                                                                 \\ \ \ \ \ \ \ \ \ \ \ \ F_{12}=\frac{Kq_1q_2}{r^2}\hat r_{12}\\ \\ \\ here, \ \hat r_{12}=\frac{\vec r_1-\vec r_2}{|r_1-r_2|}=\frac{\vec r_{12}}{r}\\ \\ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ F_{12}=\frac{Kq_1.q_2}{r^3}\vec r_{12}

 

Force when dielectric inserted between the charges: 

When a dielectric of dielectric constant k is completely filled between the charges then force 

                                                                         F_{med}=\frac{q_{1}q_{2}}{4\pi \varepsilon _{0}kr^{2}}=\frac{q_{1}q_{2}}{4\pi \varepsilon _{0}\epsilon_rr^{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_1Q_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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Coulomb's Law

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