Bending the stick stretches the chemical bonds holding the stick's atoms together, which provides a source of elastic energy.

Consider a uniformly charged sphere of radius Rand total charge Q. The electric field Eout outsidethe sphere (r≥R) is simply tha

AlexFokin [52]

1) Electric potential inside the sphere: $\frac{Q}{8\pi \epsilon_0 R}(3-\frac{r^2}{R^2})$

2) Ratio Vcenter/Vsurface: 3/2

3) Find graph in attachment

Explanation:

1)

The electric field inside the sphere is given by

$E=\frac{1}{4\pi \epsilon_0}\frac{Qr}{R^3}$

where

$\epsilon_0=8.85\cdot 10^{-12}F/m$ is the vacuum permittivity

Q is the charge on the sphere

R is the radius of the sphere

r is the distance from the centre at which we compute the field

For a radial field,

$E(r)=-\frac{dV(r)}{dr}$

Therefore, we can find the potential at distance r by integrating the expression for the electric field. Calculating the difference between the potential at r and the potential at R,

$V(R)-V(r)=-\int\limits^R_r E(r)dr=-\frac{Q}{4\pi \epsilon_0 R^3}\int r dr = \frac{-Q}{8\pi \epsilon_0 R^3}(R^2-r^2)$

The potential at the surface, V(R), is that of a point charge, so

$V(R)=\frac{Q}{4\pi \epsilon_0 R}$

Therefore we can find the potential inside the sphere, V(r):

$V(r)=V(R)+\Delta V=\frac{Q}{4\pi \epsilon_0 R}+\frac{-Q}{8\pi \epsilon_0 R^3}(R^2-r^2)=\frac{Q}{8\pi \epsilon_0 R}(3-\frac{r^2}{R^2})$

2)

At the center,

r = 0

Therefore the potential at the center of the sphere is:

$V(r)=\frac{Q}{8\pi \epsilon_0 R}(3-\frac{r^2}{R^2})\\V(0)=\frac{3Q}{8\pi \epsilon_0 R}$

On the other hand, the potential at the surface is

$V(R)=\frac{Q}{4\pi \epsilon_0 R}$

Therefore, the ratio V(center)/V(surface) is:

$\frac{V(0)}{V(R)}=\frac{\frac{3Q}{8\pi \epsilon_0 R}}{\frac{Q}{4\pi \epsilon_0 R}}=\frac{3}{2}$

3)

The graph of V versus r can be found in attachment.

We observe the following:

- At r = 0, the value of the potential is $\frac{3}{2}V(R)$ , as found in part b) (where $V(R)=\frac{Q}{4\pi \epsilon_0 R}$ )

- Between r and R, the potential decreases as $-\frac{r^2}{R^2}$

- Then at r = R, the potential is $V(R)$

- Between r = R and r = 3R, the potential decreases as $\frac{1}{R}$ , therefore when the distance is tripled (r=3R), the potential as decreased to 1/3 ( $\frac{1}{3}V(R)$ )

Learn more about electric fields and potential:

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7 0

3 years ago

Please help me I have to send for my teacher

expeople1 [14]

Answer:

for the fill in the blanks

1- static

2-kinetic

3-coeffiecient

4-opposite to

5-sin theta

6-cos theta

im not sure however what to do with the top part or if its even part of what you need help with

8 0

3 years ago

In a circuit of 2 lamps in parallel if the current in one lamp is 2a the current in the other lamp is?

ioda

In a circuit having 2 lamps are connected in parallel to a battery

then the two lamps will be having the same potential as the battery

i.e

$V_{1} = V_{2} = V_{battery}$

As per Ohm's law,

$I_{1} = \frac{V_{1}}{R_{1}}$ and $I_{2} = \frac{V}{R_{2} }$

In other words, each lamp's current is inversely related to its individual resistance. We only know the current in one of the bulbs in this specific instance. We would therefore need further information in order to calculate the current in the other light. Therefore, there isn't enough data to make a statement.

Under the assumption that all physical parameters, including temperature, remain constant, Ohm's law asserts that "the voltage across a conductor is directly proportional to the current flowing through it".

Learn more about Ohm's law here

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4 0

2 years ago

What is the frequency of an electromagnetic wave that has a wavelength of 300,000 km? (the speed of light is 300,000 km/s.)?

expeople1 [14]

Frequency represents the number of complete oscillations in one second. it is measured in Hertz (Hz). Electromagnetic waves are waves which do not require a material media for transmission. They travel with a speed of light.
The speed (m/s) of a wave is given by frequency (Hz) × Wavelength (m)
Speed is 300,000 km/sec or 300,000,000 m/s and the wavelength is 300,000 km or 300,000,000 m.
Frequency = speed÷ wavelength
= 300000000 ÷ 300000000 = 1
Therefore, the frequency of the wave is 1Hz

6 0

3 years ago

Give two examples of vernier calliper

omeli [17]

Answer:

Example 1, if a vernier caliper output a measurement reading of 2.13 cm, this means that: The main scale contributes the main number(s) and one decimal place to the reading

E.g. 2. 1 cm, whereby 2 is the main number and 0.1 is the one decimal place number

Explanation:

plz mark as brainliest and hope it helps you

4 0

3 years ago