A capacitor has two overlapping plates of width 4.9 m and length 3.5 m separated by 1.3 cm. A dielectric of dielectric constant ê = 58.0 fills the space between the plates. If this capacitor is connected to a 35 V battery, how much energy is stored in the capacitor when it is charged to 35 V?

I first found the capacitance using the eqn C=k*(8.854*10^-12)
*Area/distance and found C=6.67*10^-7F but when i substitute C in the equation E=1/2*CV^2 i don't get the correct answer(0.000415J.

Sorry i mean k=58 and the values i substitued into the eqn were C=58*(8.854*10^-12)*(3.5m*4.9m)/0.013m which gave me C=6.77*10^-7F

I agree with your calculation of C. Try that with

E = (1/2) C V^2
and you should get the correct energy value.

To calculate the energy stored in a capacitor, you need to use the correct formula and ensure that you have converted all the units to the appropriate SI units. Let's go through the steps again to find the correct answer.

Step 1: Calculate the capacitance (C):
You correctly used the formula C = k * (ε0 * A) / d, where k is the dielectric constant, ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.

Given:
- Width of the plates (W) = 4.9 m
- Length of the plates (L) = 3.5 m
- Distance between the plates (d) = 1.3 cm = 0.013 m
- Dielectric constant (k) = 58.0
- Permittivity of free space (ε0) = 8.854 * 10^-12 F/m (Farads per meter)

Calculate the area (A) of the plates:
A = W * L = 4.9 m * 3.5 m = 17.15 m^2

Now calculate the capacitance (C):
C = k * (ε0 * A) / d
C = 58.0 * (8.854 * 10^-12 F/m * 17.15 m^2) / 0.013 m
C ≈ 6.648 * 10^-7 F

Step 2: Calculate the energy stored in the capacitor (E):
You need to use the formula E = 0.5 * C * V^2, where C is the capacitance and V is the voltage across the capacitor.

Given:
- Voltage (V) = 35 V

Calculate the energy (E):
E = 0.5 * C * V^2
E = 0.5 * (6.648 * 10^-7 F) * (35 V)^2
E ≈ 0.0004188 J

Therefore, the correct answer for the energy stored in the capacitor when it is charged to 35 V is approximately 0.0004188 J.