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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

Two boats start together and race across a 48-km-wide lake and back. Boat A goes across at 48 km/h and returns at 48 km/h. Boat

nika2105 [10]

Answer:

Part 1)

Boat A will win the race

Part 2)

Boat A will win the race by 48 km as the 2nd boat will reach the other end while boat A will just touches the finish line

Part 3)

average velocity must be zero

Explanation:

As we know that the distance moved by the boat is given as

$d = 48 km$

now the time taken by the boat to move to and fro is given as

$t = \frac{d}{v}$

$t = \frac{48 + 48}{48}$

$t = 2 hrs$

Time taken by Boat B to cover the distance

$t = \frac{48}{24} + \frac{48}{72}$

$t = 2.66 h$

Part 1)

Boat A will win the race

Part 2)

Boat A will win the race by 48 km as the 2nd boat will reach the other end while boat A will just touches the finish line

Part 3)

Since the displacement of Boat A is zero

so average velocity must be zero

3 0

3 years ago

Acording to Newton’s second law of motion if a rigid body of unchanging mass is observed accelerating what must be happening

blondinia [14]

A force is being applied to the mass.

6 0

3 years ago

Read 2 more answers

A ball is thrown straight up with a speed of 30

konstantin123 [22]

Answer:

A ball is thrown straight up with a speed of 30

m/s. What is the maximum height reached by

the ball?

4 0

2 years ago

Determine which heat transfers below are due to the process of conduction. I) You walk barefoot on the hot street and it burns y

Taya2010 [7]

Answer:

I) You walk barefoot on the hot street and it burns your toes.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.

Explanation:

In conduction mode of heat transfer we know that the energy is transferred from one system to other system due to direct contact of two bodies

Here due to this direct contact the energy is transferred via a given solid or liquid medium

In this type of heat transfer medium particles will remain in its own position only the energy is transferred.

So here we can say the correct answer will be

I) You walk barefoot on the hot street and it burns your toes.

II) When you get into a car with hot black leather in the middle of the summer and your skin starts to get burned.

3 0

3 years ago