Electrostatic Potential And Capacitance

The fringe width in a double slit experiment is given by the formula: Where:
is the wavelength of the light,
is the distance between the slits and the screen,
is the distance between the slits.

For the wavelength , , and , we can calculate the fringe width: The distance of the third bright fringe from the central maximum is: Thus, the distance of the third bright fringe is 1.8 mm.

Let be the angle of the prism, the angle of incidence on the face AB, and the angle of emergence. The angle of deviation is the angle between the incident and emergent rays. For this case, we are given that and the prism angle . Using the formula for the deviation angle in a prism: Given that the emergent ray is normal to the face AC, we have . Therefore, we can substitute into the formula: Solving for : Using Snell’s law to find the refractive index of the material of the prism: Where is the angle of refraction inside the prism. Since , we can substitute the known values to find the refractive index of the material of the prism.

The magnification produced by a mirror is given by the formula: Where:
is the image distance,
is the object distance.

Given that the image is real and enlarged, the image distance is positive, and the object distance is negative. The condition that the image just touches the pencil means the image and object distances add up to the focal length. Therefore: Also, the relationship between the focal length , object distance , and image distance for a mirror is given by the mirror equation: From these two equations, we can calculate the magnification produced by the mirror.

Problem: Finding Unknown Charge Using Electric Potential

Given:

• at position
• is an unknown charge at position
• Point of interest:
• Total potential at point is zero.

Step 1: Formula for Electric Potential

Electric potential due to a point charge at a distance is:

Step 2: Distances from Point of Interest

• Distance from to point:
• Distance from to point: (since from to )

Step 3: Total Electric Potential

The total potential at the point is the sum of potentials from both charges:

Substitute values:

Final Answer:

The required charge is: placed at

Total Work Done in Moving Charges

Given:

• Equilateral triangle side:
• Charges:

Step 1: Initial Potential Energy ( )

Formula:

Substitute values:

Step 2: Final Potential Energy ( )

New distance between charges (midpoints):

Step 3: Work Done

Using the formula :

Final Answer:

Total Work Done: