Answer
Verified
350.7k+ views
Hint:Let us first talk about charge. When matter is put in an electromagnetic field, it acquires an electric charge, which causes it to undergo a force. Positive and negative charges are the two forms of electric charge commonly carried by protons and electrons respectively.
Complete step by step answer:
The electrostatic force $F$ between two point charges ${q_1}$ and ${q_2}$ is proportional to the product of their magnitudes and inversely proportional to the square of their distance. Like charges repel one another, while opposite charges draw one another.
$F = k\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
Here, $F = $electric force, $k = $Coulomb constant, ${q_{1,}}{q_2} = $Charges and $r = $Distance of separation.
Now, let us solve the problem: Let "$r$" be the distance between the charge $q$ and the equilibrium state of $Q$.
Total Force acting on Charge $q$ and $4q$:
$F = \dfrac{{kqQ}}{{{r^2}}} + \dfrac{{k4qQ}}{{{{(l - r)}^2}}}$
For \[Q\] to be in equilibrium, $F$ should be equated to zero.
$\dfrac{{kqQ}}{{{r^2}}} + \dfrac{{k4qQ}}{{{{(l - r)}^2}}} = 0$
$\Rightarrow {(l - r)^2} = 4{r^2}$
$\Rightarrow l - r = 2r$...................[By taking square root both the sides]
$\therefore r = \dfrac{l}{3}$
Let's compare the equilibrium of 4q charge to find out the value of charge:
$k4qQ\dfrac{1}{{{{(l - r)}^2}}} + 4kqq\dfrac{1}{{{l^2}}} = 0$
$\therefore Q = - \dfrac{{4q}}{9}$
Hence, the charge $Q$ needed to achieve equilibrium for the entire system is $-\dfrac{{4q}}{9}$ and it should be placed at a distance of $\dfrac{l}{3}$ from charge $q$.
Note:To determine the direction of the force, you must apply the rule of attraction, which states that opposite charges attract and equal charges repel. Two opposite charges (positive and negative) repel each other, while two positives (or negatives) attract each other.
Complete step by step answer:
The electrostatic force $F$ between two point charges ${q_1}$ and ${q_2}$ is proportional to the product of their magnitudes and inversely proportional to the square of their distance. Like charges repel one another, while opposite charges draw one another.
$F = k\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
Here, $F = $electric force, $k = $Coulomb constant, ${q_{1,}}{q_2} = $Charges and $r = $Distance of separation.
Now, let us solve the problem: Let "$r$" be the distance between the charge $q$ and the equilibrium state of $Q$.
Total Force acting on Charge $q$ and $4q$:
$F = \dfrac{{kqQ}}{{{r^2}}} + \dfrac{{k4qQ}}{{{{(l - r)}^2}}}$
For \[Q\] to be in equilibrium, $F$ should be equated to zero.
$\dfrac{{kqQ}}{{{r^2}}} + \dfrac{{k4qQ}}{{{{(l - r)}^2}}} = 0$
$\Rightarrow {(l - r)^2} = 4{r^2}$
$\Rightarrow l - r = 2r$...................[By taking square root both the sides]
$\therefore r = \dfrac{l}{3}$
Let's compare the equilibrium of 4q charge to find out the value of charge:
$k4qQ\dfrac{1}{{{{(l - r)}^2}}} + 4kqq\dfrac{1}{{{l^2}}} = 0$
$\therefore Q = - \dfrac{{4q}}{9}$
Hence, the charge $Q$ needed to achieve equilibrium for the entire system is $-\dfrac{{4q}}{9}$ and it should be placed at a distance of $\dfrac{l}{3}$ from charge $q$.
Note:To determine the direction of the force, you must apply the rule of attraction, which states that opposite charges attract and equal charges repel. Two opposite charges (positive and negative) repel each other, while two positives (or negatives) attract each other.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Write a letter to the principal requesting him to grant class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Difference Between Plant Cell and Animal Cell
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE