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A solid nonconducting sphere of radius R has a charge Q uniformly distributed throughout its volume. A Gaussian surface of radiu

anyanavicka [17]

Answer:

1. E x 4πr² = ( Q x r³) / ( R³ x ε₀ )

Explanation:

According to the problem, Q is the charge on the non conducting sphere of radius R. Let ρ be the volume charge density of the non conducting sphere.

As shown in the figure, let r be the radius of the sphere inside the bigger non conducting sphere. Hence, the charge on the sphere of radius r is :

Q₁ = ∫ ρ dV

Here dV is the volume element of sphere of radius r.

Q₁ = ρ x 4π x ∫ r² dr

The limit of integration is from 0 to r as r is less than R.

Q₁ = (4π x ρ x r³ )/3

But volume charge density, ρ = $\frac{3Q}{4\pi R^{3} }$

So, $Q_{1} = \frac{Qr^{3} }{R^{3} }$

Applying Gauss law of electrostatics ;

∫ E ds = Q₁/ε₀

Here E is electric field inside the sphere and ds is surface element of sphere of radius r.

Substitute the value of Q₁ in the above equation. Hence,

E x 4πr² = ( Q x r³) / ( R³ x ε₀ )

7 0

3 years ago

The mass of the Sun is 1. 99 × 1030 kg. Jupiter is 7. 79 × 108 km away from the Sun and has a mass of 1. 90 × 1027 kg. The gravi

german

The gravitational force is s type of force that has the ability to attract any two objects having mass. The gravitational force will be $4.16\times10^{23}$ .

<h3>What is the gravitational force?</h3>

The gravitational force is s type of force that has the ability to attract any two objects with mass. Gravitational force tries to pull two masses towards each other.

$F= G\frac{m_1m_2}{r^{2} }$

Given,

mass of the sun ( $m_1$ )= $1.99\times10^{23}$ kg

mass of Jupiter( $m_2$ )= $7.79\times10^{8}$ kg

distance between the sun and Jupiter (r)= $1.90\times10^{27}$ m

$F= G\frac{m_1m_2}{r^{2} }\\\\\\F=4.16\times10^{23}\times\frac{1.99\times10^{23}\times7.79\times10^{8}}{({1.90\times10^{27})^2} }$

$F= 4.16\times(10)^{23}$ Newton

Hence the gravitational force between the sun and Jupiter will be $4.16\times10^{23}$

To learn more about gravitational force refer to the link:

brainly.com/question/24783651

4 0

2 years ago

Assume that the speed of light in a vacuum has the hypothetical value of 18.0 m/s. A car is moving at a constant speed of 14.0 m

denis23 [38]

Answer:

4.245s

Explanation:

Given that,

Hypothetical value of speed of light in a vacuum is 18 m/s

Speed of the car, 14 m/s

Time given is 6.76 s, and we're asked to find the observed time, T

The relationship between the two times can be given as

T = t / √[1 - (v²/c²)]

The missing variable were looking for is t, and we can find it if we rearrange the formula and make t the subject

t = T / √[1 - (v²/c²)]

And now, we substitute the values and insert into the equation

t = 6.76 * √[1 - (14²/18²)]

t = 6.76 * √[1 - (196/324)]

t = 6.76 * √(1 - 0.605)

t = 6.76 * √0.395

t = 6.76 * 0.628

t = 4.245 s

Therefore, the time the driver measures for the trip is 4.245s

8 0

3 years ago

If an engine does 660 J of work in 10 seconds, its average power is ...

givi [52]

Answer:

66w

Explanation:

p=w/t

p=660/10

p=66

prolly a bad explanation but hope it helps...

4 0

2 years ago

Location A receives

Vlad1618 [11]

Location A receives more rainfall than Location B due to the rain shadow effect.

<u>Explanation</u>:

Rain shadow effect is caused due to the presence of mountains.
A rain shadow area is an area of land that has been forced to become dry, devoid of any vegetation growth due to the blockage of precipitation by mountains. These rain shadow areas will have a dry climate.
The other side of the mountain would receive plenty of precipitation and therefore would be flourished with plant growth. These areas will have a cool and wet climate.
In this case, Location A is on the other side of the mountain and so receives more rainfall or precipitation. Meanwhile, Location B is on the rain shadow region and so receives less rainfall.

7 0

3 years ago