A charge Q is divided into two parts q and Q-q and separated by a distance of R. The force of repulsion between them will be maximum when A)q=Q/4 B)q=Q/2 C)q=Q D)none of these Please explain.and solve it Very important?

Question

Answer

Hey it's option B  i. e   Q/2

Answer

Explanation:

The force of repulsion between two charges is given by Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

F = k(q1q2)/r^2

where F is the force, q1 and q2 are the charges, r is the distance between them, and k is Coulomb's constant.

To find the maximum force of repulsion between the two charges, we need to find the value of q that maximizes the product q(Q-q) and the value of r that minimizes the denominator r^2.

Solution:

Let's first find the product q(Q-q) and simplify it.

q(Q-q) = Qq - q^2

To find the maximum value of Qq - q^2, we can take the derivative with respect to q and set it equal to zero.

d(Qq - q^2)/dq = Q - 2q = 0

Solving for q, we get q = Q/2. Therefore, the maximum force of repulsion occurs when the charges are divided equally.

Now let's find the distance between the two charges that minimizes the denominator r^2. We can use the Pythagorean theorem to find the distance between the two charges.

r = sqrt[(R/2)^2 + d^2]

where d is the distance between the two charges.

To minimize r^2, we can take the derivative with respect to d and set it equal to zero.

d(r^2)/dd = 2d(R/2)^2/(R^2/4 + d^2)^(3/2) = 0

Solving for d, we get d = R/2. Therefore, the maximum force of repulsion occurs when the charges are separated by a distance of R/2.

Therefore, the answer is (A) q = Q/4.

Similar Class 12 Doubts

Charge Q is to be divided into two parts q and Q- q for what will you q will force between them be maximum at a particular distance?

let chage Q on a body is divided into two charged bodies and these body there after kept at a distance from each other .show that the force between them is maximum if Q/q =2

Two identical small spherical conductors are separated by a distance D and carry equal positive charges. half of the charge on one conductor is transferred to the other. if the force between them was of magnitude F, the force now is?

Two point charges q each separated by r in air. How electric field between them varies with distance from one charge ? Show graphically?

Two identical metal balls with charges 2Q and -Q are separated by some distance and exert a force F on each other.They are joined by a conducting wire and then separeted by some distance. What is the force between them now?

Top Courses for Class 12

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams