A certain charge 2Q is divided at first into | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the total charge be $2Q$. The two parts are $q_{1}$ and $q_{2}$,such that $q_{1} + q_{2} = 2Q$. Thus,$q_{2} = 2Q - q_{1}$.According to Coulomb

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let the total charge be $2Q$. The two parts are $q_{1}$ and $q_{2}$,such that $q_{1} + q_{2} = 2Q$. Thus,$q_{2} = 2Q - q_{1}$.According to Coulomb's law,the force of interaction $F$ between the charges separated by a distance $r$ is given by $F = k \frac{q_{1}q_{2}}{r^2}$.Substituting $q_{2}$,we get $F = \frac{k}{r^2} (q_{1})(2Q - q_{1}) = \frac{k}{r^2} (2Qq_{1} - q_{1}^2)$.For the force $F$ to be maximum,the derivative of $F$ with respect to $q_{1}$ must be zero: $\frac{dF}{dq_{1}} = 0$.$\frac{d}{dq_{1}} [\frac{k}{r^2} (2Qq_{1} - q_{1}^2)] = \frac{k}{r^2} (2Q - 2q_{1}) = 0$.This implies $2Q - 2q_{1} = 0$,so $q_{1} = Q$.Therefore,the ratio $\frac{Q}{q_{1}} = \frac{Q}{Q} = 1$.

$A$ certain charge $2Q$ is divided at first into two parts $q_{1}$ and $q_{2}$. Later,the charges are placed at a certain distance. If the force of interaction between the two charges is maximum,then find the value of $\frac{Q}{q_{1}}$.

Similar Questions

Two identical conducting spheres $A$ and $B$ having charges $+q$ and $-q$ respectively are kept at a distance $d$ apart and experience a Coulombian force $F$ between them. If $50\%$ of the charge is transferred from sphere $B$ to $A$,then the new Coulombian force between them is . . . . . . .

If the distance between two equal point charges is doubled,what would happen to the force between them?

For any fixed distance,the electromagnetic force between two protons is $10^n$ times the gravitational force between them. Then $n=$

The electrical force between two point charges is $200 \ N$. If we increase $10 \ \%$ charge on one of the charges and decrease $10 \ \%$ charge on the other,then the electrical force between them for the same distance becomes . . . . . . . . . . (in $N$)

Charges $3Q$,$q$,and $Q$ are placed along the $x$-axis at positions $x=0$,$x=l/3$,and $x=l$ respectively. When the net force on charge $Q$ is zero,the value of $q$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module