Scelta multipla
Which of the following is the correct SI unit for measuring electric current flow?
118
views
24. Electric Force & Field; Gauss' Law
Electric Charge
Scelta multipla
A conducting sphere with a diameter of is charged so that its electric potential is relative to infinity. What is the total charge on the sphere? (Assume the sphere is isolated in air, and use for the permittivity of free space.)
A
B
C
D
Guida verificata passo dopo passo1
Identify the given quantities: the diameter of the conducting sphere is 4.00 cm, so the radius \(r\) is half of that, which is \(r = \frac{4.00}{2} = 2.00\) cm. Convert this to meters for SI units: \(r = 2.00 \times 10^{-2}\) m. The electric potential \(V\) of the sphere relative to infinity is 50 V.
Recall the formula for the electric potential \(V\) on the surface of a charged conducting sphere of radius \(r\) carrying charge \(Q\) in vacuum (or air):
\(V = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r}\)
where \(\varepsilon_0\) is the permittivity of free space.
Rearrange the formula to solve for the total charge \(Q\) on the sphere:
\(Q = 4 \pi \varepsilon_0 r V\)
Substitute the known values into the equation: use \(\varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2\), \(r = 2.00 \times 10^{-2}\) m, and \(V = 50\) V.
Calculate the product step-by-step to find the total charge \(Q\) on the sphere, ensuring units are consistent and the final charge is expressed in coulombs (C).
Video correlati
Pratica correlata
