An energy of 6.0×10−2 J is stored in the metal sphere on top of a Van de Graaff generator. A spark carrying 1.0 micro-coulomb (1.0×10−6 C) discharges the sphere.Find the sphere's potential relative to ground.
last one for the night
Well, well, well, looks like someone's trying to zap me with a tricky question before bedtime! Alright, challenge accepted!
To find the sphere's potential relative to ground, we can use the formula for electric potential energy (U) given by U = qV, where q is the charge and V is the potential. In this case, the charge is 1.0×10^(-6) C and the energy is 6.0×10^(-2) J.
Rearranging the formula, we get V = U/q. Plugging in the values, we have V = (6.0×10^(-2) J) / (1.0×10^(-6) C).
Calculating this, we get V ≈ 60,000 V.
So, the potential of that metal sphere relative to ground is approximately 60,000 volts! That's electrifying! Sleep tight!
To find the potential of the sphere relative to ground, we can use the formula:
Potential = Energy / Charge
Given:
Energy = 6.0 × 10^-2 J
Charge = 1.0 × 10^-6 C
Substituting the values into the formula, we get:
Potential = (6.0 × 10^-2 J) / (1.0 × 10^-6 C)
Simplifying the expression, we have:
Potential = 6.0 × 10^4 J/C
Therefore, the sphere's potential relative to ground is 6.0 × 10^4 J/C.
To find the sphere's potential relative to ground, we can make use of the formula that relates energy and electric potential. The formula is:
E = Q * V
Where:
- E is the energy stored in the metal sphere (6.0×10^(-2) J).
- Q is the charge that discharges through the sphere (1.0×10^(-6) C).
- V is the potential difference or electric potential we are trying to find.
Rearranging the formula, we get:
V = E / Q
Substituting the given values, we have:
V = 6.0×10^(-2) J / 1.0×10^(-6) C
To simplify this expression, divide 6.0 by 1.0, which equals 6.0:
V = 6.0 × 10^(-2-(-6))
Next, we subtract the exponents: -2 - (-6) = -2 + 6 = 4:
V = 6.0 × 10^4
Therefore, the sphere's potential relative to ground is 6.0 × 10^4 volts.
Energy = Q*V
V = Energy/Q = 6*10^-2/10^-6 = 60,000 V