Answer:
The Earth is toward the sun
Explanation:
DONT LISTEN TO ME I AM A CHILD AND I JUST GUESSED
Answer:
Explanation:
From the given information:
We know that the thin spherical shell is on a uniform surface which implies that both the inside and outside the charge of the sphere are equal, Then
The volume charge distribution relates to the radial direction at r = R
∴
![\rho (r) \ \alpha \ \delta (r -R)](https://tex.z-dn.net/?f=%5Crho%20%28r%29%20%5C%20%20%5Calpha%20%20%5C%20%20%5Cdelta%20%28r%20-R%29)
![\rho (r) = k \ \delta (r -R) \ \ at \ \ (r = R)](https://tex.z-dn.net/?f=%5Crho%20%28r%29%20%3D%20k%20%5C%20%20%5Cdelta%20%28r%20-R%29%20%5C%20%5C%20%20at%20%5C%20%5C%20%20%28r%20%3D%20R%29)
![\rho (r) = 0\ \ since \ r< R \ \ or \ \ r>R---- (1)](https://tex.z-dn.net/?f=%5Crho%20%28r%29%20%3D%200%5C%20%5C%20since%20%5C%20r%3C%20R%20%20%5C%20%5C%20or%20%20%5C%20%5C%20r%3ER----%20%281%29)
To find the constant k, we examine the total charge Q which is:
![Q = \int \rho (r) \ dV = \int \sigma \times dA](https://tex.z-dn.net/?f=Q%20%3D%20%5Cint%20%5Crho%20%28r%29%20%5C%20dV%20%3D%20%5Cint%20%5Csigma%20%5Ctimes%20dA)
![Q = \int \rho (r) \ dV = \sigma \times4 \pi R^2](https://tex.z-dn.net/?f=Q%20%3D%20%5Cint%20%5Crho%20%28r%29%20%5C%20dV%20%3D%20%5Csigma%20%5Ctimes4%20%5Cpi%20R%5E2)
∴
![\int ^{2 \pi}_{0} \int ^{\pi}_{0} \int ^{R}_{0} \rho (r) r^2sin \theta \ dr \ d\theta \ d\phi = \sigma \times 4 \pi R^2](https://tex.z-dn.net/?f=%5Cint%20%5E%7B2%20%5Cpi%7D_%7B0%7D%20%5Cint%20%5E%7B%5Cpi%7D_%7B0%7D%20%5Cint%20%5E%7BR%7D_%7B0%7D%20%5Crho%20%28r%29%20r%5E2sin%20%5Ctheta%20%20%5C%20dr%20%5C%20d%5Ctheta%20%5C%20d%5Cphi%20%3D%20%5Csigma%20%5Ctimes%204%20%5Cpi%20R%5E2)
![\int^{2 \pi}_{0} d \phi* \int ^{\pi}_{0} \ sin \theta d \theta * \int ^{R}_{0} k \delta (r -R) * r^2dr = \sigma \times 4 \pi R^2](https://tex.z-dn.net/?f=%5Cint%5E%7B2%20%5Cpi%7D_%7B0%7D%20d%20%5Cphi%2A%20%5Cint%20%5E%7B%5Cpi%7D_%7B0%7D%20%5C%20sin%20%5Ctheta%20d%20%5Ctheta%20%2A%20%5Cint%20%5E%7BR%7D_%7B0%7D%20k%20%5Cdelta%20%28r%20-R%29%20%2A%20r%5E2dr%20%3D%20%5Csigma%20%5Ctimes%204%20%5Cpi%20R%5E2)
![(2 \pi)(2) * \int ^{R}_{0} k \delta (r -R) * r^2dr = \sigma \times 4 \pi R^2](https://tex.z-dn.net/?f=%282%20%5Cpi%29%282%29%20%2A%20%5Cint%20%5E%7BR%7D_%7B0%7D%20k%20%5Cdelta%20%28r%20-R%29%20%2A%20r%5E2dr%20%3D%20%5Csigma%20%5Ctimes%204%20%5Cpi%20R%5E2)
Thus;
![k * 4 \pi \int ^{R}_{0} \delta (r -R) * r^2dr = \sigma \times R^2](https://tex.z-dn.net/?f=k%20%2A%204%20%5Cpi%20%20%5Cint%20%5E%7BR%7D_%7B0%7D%20%20%5Cdelta%20%28r%20-R%29%20%2A%20r%5E2dr%20%3D%20%5Csigma%20%5Ctimes%20%20R%5E2)
![k * \int ^{R}_{0} \delta (r -R) r^2dr = \sigma \times R^2](https://tex.z-dn.net/?f=k%20%2A%20%5Cint%20%5E%7BR%7D_%7B0%7D%20%20%5Cdelta%20%28r%20-R%29%20%20r%5E2dr%20%3D%20%5Csigma%20%5Ctimes%20%20R%5E2)
![k * R^2= \sigma \times R^2](https://tex.z-dn.net/?f=k%20%2A%20R%5E2%3D%20%5Csigma%20%5Ctimes%20%20R%5E2)
![k = R^2 --- (2)](https://tex.z-dn.net/?f=k%20%20%3D%20%20%20R%5E2%20---%20%282%29)
Hence, from equation (1), if k = ![\sigma](https://tex.z-dn.net/?f=%5Csigma)
![\mathbf{\rho (r) = \delta* \delta (r -R) \ \ at \ \ (r=R)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Crho%20%28r%29%20%3D%20%5Cdelta%2A%20%5Cdelta%20%28r%20-R%29%20%20%5C%20%5C%20%20at%20%20%20%5C%20%5C%20%20%28r%3DR%29%7D)
![\mathbf{\rho (r) =0 \ \ at \ \ rR}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Crho%20%28r%29%20%3D0%20%5C%20%5C%20%20at%20%20%20%5C%20%5C%20%20r%3CR%20%20%5C%20%5C%20%20or%20%5C%20%20%5C%20r%3ER%7D)
To verify the units:
![\mathbf{\rho (r) =\sigma \ * \ \delta (r-R)}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Crho%20%28r%29%20%3D%5Csigma%20%5C%20%2A%20%20%5C%20%5Cdelta%20%28r-R%29%7D)
↓ ↓ ↓
c/m³ c/m³ × 1/m
Thus, the units are verified.
The integrated charge Q
![Q = \int \rho (r) \ dV \\ \\ Q = \int ^{2 \ \pi}_{0} \int ^{\pi}_{0} \int ^R_0 \rho (r) \ \ r^2 \ \ sin \theta \ dr \ d\theta \ d \phi \\ \\ Q = \int ^{2 \pi}_{0} \ d \phi \int ^{\pi}_{0} \ sin \theta \int ^R_{0} \rho (r) r^2 \ dr](https://tex.z-dn.net/?f=Q%20%3D%20%5Cint%20%5Crho%20%28r%29%20%5C%20dV%20%5C%5C%20%5C%5C%20Q%20%3D%20%5Cint%20%5E%7B2%20%5C%20%5Cpi%7D_%7B0%7D%20%5Cint%20%5E%7B%5Cpi%7D_%7B0%7D%20%5Cint%20%5ER_0%20%5Crho%20%28r%29%20%5C%20%5C%20r%5E2%20%5C%20%5C%20%20sin%20%5Ctheta%20%20%5C%20dr%20%5C%20d%5Ctheta%20%5C%20%20d%20%5Cphi%20%20%5C%5C%20%5C%5C%20%20Q%20%3D%20%5Cint%20%5E%7B2%20%5Cpi%7D_%7B0%7D%20%5C%20%20d%20%5Cphi%20%20%5Cint%20%5E%7B%5Cpi%7D_%7B0%7D%20%5C%20sin%20%5Ctheta%20%20%5Cint%20%5ER_%7B0%7D%20%5Crho%20%28r%29%20r%5E2%20%5C%20dr)
![Q = (2 \pi) (2) \int ^R_0 \sigma * \delta (r-R) r^2 \ dr](https://tex.z-dn.net/?f=Q%20%3D%20%282%20%5Cpi%29%20%282%29%20%5Cint%20%5ER_0%20%5Csigma%20%2A%20%5Cdelta%20%28r-R%29%20r%5E2%20%5C%20dr)
![Q = 4 \pi \sigma \int ^R_0 * \delta (r-R) r^2 \ dr](https://tex.z-dn.net/?f=Q%20%3D%204%20%5Cpi%20%20%5Csigma%20%20%5Cint%20%5ER_0%20%20%2A%20%5Cdelta%20%28r-R%29%20r%5E2%20%5C%20dr)
since ![( \int ^{xo}_{0} (x -x_o) f(x) \ dx = f(x_o) )](https://tex.z-dn.net/?f=%28%20%5Cint%20%5E%7Bxo%7D_%7B0%7D%20%28x%20-x_o%29%20f%28x%29%20%5C%20dx%20%3D%20f%28x_o%29%20%29)
![\mathbf{Q = 4 \pi R^2 \sigma }](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%204%20%5Cpi%20R%5E2%20%20%5Csigma%20%20%7D)
21) Acceleration from D to E: ![1 m/s^2](https://tex.z-dn.net/?f=1%20m%2Fs%5E2)
22) The acceleration of the bus from D to E is ![1 m/s^2](https://tex.z-dn.net/?f=1%20m%2Fs%5E2)
Explanation:
21)
The acceleration of an object is equal to the rate of change of velocity of the object. Mathematically:
![a=\frac{v-u}{t}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv-u%7D%7Bt%7D)
where
u is the initial velocity
v is the final velocity
t is the time elapsed
In this problem, we want to measure the acceleration of the bus from point D to point E. We have:
- Initial velocity at point D: u = 0
- Final velocity at point E: v = 5 m/s
- Time elapsed from D to E: t = 21 - 16 = 5 s
Therefore, the acceleration between D and E is
![a=\frac{5-0}{5}=1 m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B5-0%7D%7B5%7D%3D1%20m%2Fs%5E2)
22) This question is the same as 21), so the result is the same.
Learn more about acceleration:
brainly.com/question/9527152
brainly.com/question/11181826
brainly.com/question/2506873
brainly.com/question/2562700
#LearnwithBrainly
The charge of the object must be ![1.11 \times e^{-5} \text { coulomb }](https://tex.z-dn.net/?f=1.11%20%5Ctimes%20e%5E%7B-5%7D%20%5Ctext%20%7B%20coulomb%20%7D)
Answer: Option C
<u>Explanation:</u>
Suppose an electric charge can be represented by the symbol Q. This electric charge generates an electric field; Because Q is the source of the electric field, we call this as source charge. The electric field strength of the source charge can be measured with any other charge anywhere in the area. The test charges used to test the field strength.
Its quantity indicated by the symbol q. In the electric field, q exerts an electric, either attractive or repulsive force. As usual, this force is indicated by the symbol F. The electric field’s magnitude is simply defined as the force per charge (q) on Q.
![Electric field, E=\frac{\text { Force }(F)}{q}](https://tex.z-dn.net/?f=Electric%20field%2C%20E%3D%5Cfrac%7B%5Ctext%20%7B%20Force%20%7D%28F%29%7D%7Bq%7D)
Here, given E = 4500 N/C and F = 0.05 N.
We need to find charge of the object (q)
By substituting the given values, we get
![q=\frac{F}{E}=\frac{0.05 N}{4500 \mathrm{N} / \mathrm{c}}=1.11 \times e^{-5} \text { coulomb }](https://tex.z-dn.net/?f=q%3D%5Cfrac%7BF%7D%7BE%7D%3D%5Cfrac%7B0.05%20N%7D%7B4500%20%5Cmathrm%7BN%7D%20%2F%20%5Cmathrm%7Bc%7D%7D%3D1.11%20%5Ctimes%20e%5E%7B-5%7D%20%5Ctext%20%7B%20coulomb%20%7D)
Answer:
F = 800N
the magnitude of the average force exerted on the wall by the ball is 800N
Explanation:
Applying the impulse-momentum equation;
Impulse = change in momentum
Ft = m∆v
F = (m∆v)/t
Where;
F = force
t = time
m = mass
∆v = v2 - v1 = change in velocity
Given;
m = 0.80 kg
t = 0.050 s
The ball strikes the wall horizontally with a speed of 25 m/s, and it bounces back with this same speed.
v2 = 25 m/s
v1 = -25 m/s
∆v = v2 - v1 = 25 - (-25) m/s = 25 +25 = 50 m/s
Substituting the values;
F = (m∆v)/t
F = (0.80×50)/0.05
F = 800N
the magnitude of the average force exerted on the wall by the ball is 800N