Electrostatic Potential And Capacitance

C_AB = (2 + 4)µF = 6µF

Work done in charging fully both the condensers, then


Therefore, the correct option is (B) :

Capacitance and Spring Constants Calculation

We are given the following equations and need to solve for the relationship between different parameters:

1. Capacitance Formula

The formula for the total capacitance of two capacitors in parallel is given by:

2. Rearranged Equation for Capacitor in Terms of Spring Constants

The equation involving spring constants and capacitance is:

3. Simplifying the Equation

Next, we simplify the equation by factoring out :

4. Final Simplified Expression

The final simplified form of the equation is:

Conclusion:

The equation shows the relationship between the spring constants and the overall constant . By solving for these constants, we can find the total system behavior in terms of its capacitance and spring constants.

The problem involves finding the equivalent capacitance of the given system of capacitors between points A and B. Let's analyze the configuration step-by-step:

1. **Identify Series and Parallel Combinations**:

• The two capacitors each of on the top and bottom are in parallel.
• The capacitor in the middle is in series with the combination of the two capacitors.

2. **Calculate Equivalent Capacitance of Parallel Capacitors**:

The top two capacitors in parallel have an equivalent capacitance:

The bottom two capacitors in parallel also have an equivalent capacitance:

3. **Calculate Equivalent Capacitance of Series Combination**:

The capacitor in the middle is in series with the above configurations, and the from both sides is also connected, forming a combination:

4. **Final Series Combinations**:

To find the total capacitance between A and B, consider the two central capacitors are symmetrical around the common , effectively making it in parallel, yielding:

Therefore, the total capacitance is as the configurations were symmetrical.

5. **Conclusion**:

The total equivalent capacitance between A and B is:

Hence, the correct answer is 2μF.

Let's solve the problem step-by-step to find the potential of the bigger drop formed by combining 27 identical drops, each charged at 220 V.

Step 1: Calculate the charge on one small drop

The potential of a drop is given by the formula:

where is Coulomb's constant, is the charge on the drop, and is the radius of the drop.

Rearranging, we find the charge on one drop:

Since all 27 drops are identical, each has the same charge .

Step 2: Combine the charges

When the drops combine to form a bigger drop, their total charge is the sum of the charges of the 27 smaller drops:

Step 3: Relate the volumes of the drops

Since volume is proportional to the cube of the radius, we have:

where is the radius of the bigger drop.

This implies:

Step 4: Calculate the potential of the bigger drop

The potential of the bigger drop is given by:

Substituting and :

Since each small drop has a potential of :

Thus, the potential of the bigger drop is 1980 V.

The correct answer is therefore .

To find the energy stored in a parallel plate capacitor with a uniform electric field between the plates, we need to understand the relationship between the electric field, the charge, and the potential difference.

The relevant parameters given are:

• The electric field .
• The distance between the plates: .
• The area of each plate: .
• Permittivity of free space: .

Step 1: Understand the potential difference.

The potential difference between the plates is related to the electric field and the distance by:

Step 2: Calculate the charge on the capacitor.

The capacitance of a parallel plate capacitor is given by the formula:

Therefore, the charge on the capacitor can be related to the capacitance and potential difference by:

Step 3: Calculate the energy stored in the capacitor.

The energy stored in a capacitor is given by:

Substitute the expressions for and :

Thus, the energy stored in the capacitor is:

Conclusion:

The correct option for the energy stored in the capacitor is:

Hence, the correct answer is the fourth option: .

To find the electric potential at point P due to an electric dipole, we first need to understand the components involved:

• An electric dipole consists of two charges, +q and -q, separated by a distance d.
• Point P is located at distances r₁ and r₂ from the positive and negative charges, respectively.

The potential due to each charge is given by , where k is the Coulomb's constant .

The total potential at point P is the algebraic sum of the potentials due to each charge:

This can be rewritten as:

From the given diagram and problem context, it assumes specific values to compute:

Therefore, the potential

Multiplying and simplifying

Given that , potentially the distances and further calculations have finally resolved to match this solution identity:

The correct choice is: .