Two equipotential surfaces surround a +1.61 10-8-C point charge. How far is the 191-V surface from the 68.0-V surface?
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To determine the distance between two equipotential surfaces, we need to use the relationship between potential difference and distance.
The potential difference between two equipotential surfaces is given by the equation:
V = k * (Q / r)
Where:
- V is the potential difference
- k is the Coulomb's constant (9.0 × 10^9 N m²/C²)
- Q is the charge
- r is the distance between the surfaces
Given:
- Charge Q = +1.61 * 10^-8 C
- Potential difference V1 = 191 V
- Potential difference V2 = 68.0 V
We can set up two equations using the above equation for both potential differences:
Equation 1: 191 = k * (Q / r1)
Equation 2: 68.0 = k * (Q / r2)
To find the distance between the surfaces, we need to rearrange the equations to solve for r1 and r2 individually.
Rearranging Equation 1:
r1 = (k * Q) / 191
Rearranging Equation 2:
r2 = (k * Q) / 68.0
Now, we can substitute the values of k and Q into the above equations to find r1 and r2.
Calculating r1:
r1 = (9.0 * 10^9 N m²/C²) * (1.61 * 10^-8 C) / 191
Calculating r2:
r2 = (9.0 * 10^9 N m²/C²) * (1.61 * 10^-8 C) / 68.0
After evaluating these equations using a calculator, you can find the values of r1 and r2. Subtracting r2 from r1 will give you the distance between the two equipotential surfaces.