**Solution:**

Given:
- Two fixed charges A and B of 5 C each
- Distance between charges A and B = 6 m
- Charge Q = -5 C
- Q is shot perpendicular to the line joining A and B through C
- Kinetic energy of Q = 0.06 J

We need to find the distance CD.

To solve this problem, we can use the principle of conservation of energy. The initial kinetic energy of charge Q is converted into potential energy when it comes to rest at point D.

**1. Calculation of the initial kinetic energy:**

The kinetic energy of charge Q is given by the equation:

K.E. = (1/2) * m * v²

where m is the mass of the charge and v is its velocity.

Since charge Q is shot perpendicular to the line joining A and B through C, its initial velocity is perpendicular to the direction of the electric field between A and B. Therefore, the electric field does no work on charge Q and its potential energy remains constant.

Hence, the initial kinetic energy of charge Q is equal to its total energy, which is given as 0.06 J.

**2. Calculation of the potential energy at point D:**

The potential energy of a charge in the electric field is given by the equation:

P.E. = q * V

where q is the charge and V is the potential difference.

At point D, the potential difference between A and D is given by:

V = k * (q1/r1 + q2/r2)

where k is the electrostatic constant, q1 and q2 are the charges, and r1 and r2 are the distances of charge Q from A and B respectively.

In this case, q1 = 5 C, q2 = -5 C, r1 = CD, and r2 = 6 - CD.

Substituting the values, we get:

V = k * (5/CD - 5/(6-CD))

**3. Equating initial kinetic energy to potential energy at point D:**

As per the principle of conservation of energy, the initial kinetic energy of charge Q is equal to its potential energy at point D.

Therefore, we can equate the initial kinetic energy (0.06 J) to the potential energy at point D:

0.06 J = -5 C * V

Substituting the value of V from the equation obtained in step 2, we get:

0.06 J = -5 C * [k * (5/CD - 5/(6-CD))]

**4. Solving the equation to find CD:**

By rearranging the equation obtained in step 3, we can solve for CD:

0.06 J = -25 C² * [k * (1/CD - 1/(6-CD))]

Simplifying further, we get:

0.06 J = -25 C² * [k * (6-CD - CD) / (CD * (6-CD))]

0.06 J = -25 C² * [k * (6-2CD) / (CD * (6-CD))]

Now, we can calculate the value of CD by substituting the known values of k and C², and solving the equation.

The final value of CD will depend on the numerical values of k and C², which are

Use energy conservation between points kinetic energy and potential energy will be conserved at these points. at d kinetic energy will become 0 as it will come to rest..