Camina con otro compañero, al mismo tiempo y al mismo paso. Quién se mueve tú o tu compañero? Razona tu respuesta
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Answer:
a) the capacitance is the same for both capacitors.
b) The potential difference between the plates for the capacitor with charge +2q, is double of the one for the capacitor with charge +q.
c) The electric field magnitude between the plates for the capacitor with charge +2q, is double of the one for the capacitor with charge +q
d) The energy stored between the plates for the capacitor with charge +2q, is 4 times the value for the one with charge +q
Explanation:
a) The capacitance of a capacitor, by definition, is as follows:
Appying Gauss' Law to one of plates, it can be showed, that the capacitance (for a parallel plates capacitor) can be expressed as follows:
C = ε*A / d
As it can be seen, it does not depend on the charge. so we conclude that the capacitance must be the same for both capacitors, due to they are identical except for the value of the charge on the plates.
b) By definition, as we said above, the capacitance is equal to the proportion between the charge of one of the plates, and the potential difference between them.
If this proportion must remain the same, and one of the capacitors has the double of the charge than the other, the potential difference must be the double also.
c) Applying Gauss' law, to the surface of one of the plates, and assuming a constant surface charge density σ, it can be showed that the electric field can be calculated as follows:
E*A = Q/ε₀ as σ=Q/A
⇒ E = σ/ε₀
As σ is directly proportional to the charge (being the area A the same), we conclude that the electric field for the capacitor with charge +2q must be the double than the one for the capacitior with charge +q.
c) The electric potential energy, stored between plates of a capacitor, can be written as follows:
If the capacitance remains the same, we can conclude that the electric potential energy for the capacitor with charge +2q, as the charge is raised to the 2nd power, must be 4 times the one for the capacitor with charge +q.
Answer:
B) 1218
Explanation:
N = Total number of turns in the solenoid
L = length of the solenoid = 34.00 cm = 0.34 m
B = magnetic field at the center of the solenoid = 9 mT = 9 x 10⁻³ T
i = current carried by the solenoid = 2.000 A
Magnetic field at the center of the solenoid is given as
N = 1218
For a cylinder that has both ends open resonant frequency is given by the following formula:
Where n is the resonance node, v is the speed of sound in air and L is the length of a cylinder.
The fundamental frequency is simply the lowest resonant frequency.
We find it by plugging in n=1:
To find what harmonic has to be excited so that it resonates at f>20Hz we simply plug in f=20 Hz and find our n:
We can see that any resonant frequency is simply a multiple of a base frequency.
Let us find which harmonic resonates with the frequency 20 Hz:
Since n has to be an integer, final answer would be 323.
Where n is the resonance node, v is the speed of sound in air and L is the length of a cylinder.
The fundamental frequency is simply the lowest resonant frequency.
We find it by plugging in n=1:
To find what harmonic has to be excited so that it resonates at f>20Hz we simply plug in f=20 Hz and find our n:
We can see that any resonant frequency is simply a multiple of a base frequency.
Let us find which harmonic resonates with the frequency 20 Hz:
Since n has to be an integer, final answer would be 323.