1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
malfutka [58]
3 years ago
15

A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/r) for r

≤r ρ(r)=0 for r≥r where ρ0=3q/πr3 is a positive constant.
Physics
1 answer:
Nadusha1986 [10]3 years ago
4 0

A)<span>
dQ = ρ(r) * A * dr = ρ0(1 - r/R) (4πr²)dr = 4π * ρ0(r² - r³/R) dr 
which when integrated from 0 to r is 
total charge = 4π * ρ0 (r³/3 + r^4/(4R)) 
and when r = R our total charge is 
total charge = 4π*ρ0(R³/3 + R³/4) = 4π*ρ0*R³/12 = π*ρ0*R³ / 3 
and after substituting ρ0 = 3Q / πR³ we have 
total charge = Q ◄ 

B) E = kQ/d² 
since the distribution is symmetric spherically 

C) dE = k*dq/r² = k*4π*ρ0(r² - r³/R)dr / r² = k*4π*ρ0(1 - r/R)dr 
so 
E(r) = k*4π*ρ0*(r - r²/(2R)) from zero to r is 
and after substituting for ρ0 is 
E(r) = k*4π*3Q(r - r²/(2R)) / πR³ = 12kQ(r/R³ - r²/(2R^4)) 
which could be expressed other ways. 

D) dE/dr = 0 = 12kQ(1/R³ - r/R^4) means that 
r = R for a min/max (and we know it's a max since r = 0 is a min). 

<span>E) E = 12kQ(R/R³ - R²/(2R^4)) = 12kQ / 2R² = 6kQ / R² </span></span>

You might be interested in
If the speed of a wave doubles while the frequency remains the same, it means
sattari [20]

Answer:

Explanation:

Velocity of a wave is describe as

velocity =Frequency × Wavelength

Mathematically

v = fλ

Hence, Frequency, F = v / λ

Wavelength λ = v/f

So, if the frequency is kept constant, wavelength of the wave becomes directly proportional to velocity of the wave.

And this implies that, as the speed double, the wavelength is double.

5 0
3 years ago
A cylindrical tungsten filament 14.0 cmcm long with a diameter of 1.00 mmmm is to be used in a machine for which the temperature
Advocard [28]

Answer:

Resistivity ρ=1.12 x 10^-4 Ωm

Explanation:

ρ= RA/l, where R is resistance, A is cross sectional area and l is length

A=πr^2

Note Current is given R is proportion to temperature and inversely proportional to Current R=(20+273)/14*10^-2 =2000Ω

⇒ρ=R*πr^2/l all length in metre.

8 0
3 years ago
A book is launched up along the rough incline. Kinetic energy given to a book at initial point is 100 J. Book comes to stop at s
den301095 [7]

Answer:

(A) 60 J

Explanation:

At state 1

KE₁=100 J

At state 2

KE₂ = 0

U₂=80 J

Given that surface is rough so friction force will act in opposite to the direction of motion

Lets take work done by friction = Wfr

From work power energy

Work done by all forces = Change in kinetic energy

Wfr + U₂=ΔKE

Wfr+80 = 100

Wfr= 20 J

Now when book slides from top position then

Wfr+ U = KEf - KEi

-20 + 80 = KEf-0

KEf= 60 J

(A) 60 J

7 0
3 years ago
Evaluate tan45/tan45
SIZIF [17.4K]

I'm not sure I completely understand the expression you want evaluated.

It looks like a fraction with the same exact thing in both the numerator and the denominator. A fraction like that always boils down to ' 1 '.

5 0
3 years ago
Read 2 more answers
When you improve your the ability of your muscles to repeatebly exert themselves you are improving your?
Irina-Kira [14]

It is muscular endurance.

5 0
3 years ago
Other questions:
  • A circuit has a resistance of 10 Ω and current of 5 A. What is the voltage?<br><br>​
    13·1 answer
  • What planet has the least amount of inertia
    7·1 answer
  • Which is not part of nuclear chemistry? A. Strong nuclear force B. Double-replacement reactions C. Radioactivity D. Nuclear deca
    10·2 answers
  • The mass of Pluto is 1.303 times 10 to the 22 power kilograms and it had an acceleration of gravity of 0.0630 grams. What is the
    7·1 answer
  • Matter is anything that...
    6·2 answers
  • A student's pencil rolls off a desk and lands 0.47 m away from the edge of the
    15·1 answer
  • Detlev walks 1000 meters north to the store and walks back 900 meters south to his friends house. The friends house is 100 meter
    14·1 answer
  • HELPPPPP MEEEEE PLEASE I NEED TO SUBMIT IN LESS THAN 10 MINSS
    6·1 answer
  • If a 1-megaton nuclear weapon is exploded
    12·1 answer
  • You push downward on a box at an angle 25° below the horizontal with a force of 750 N. If the box is on a flat horizontal surfac
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!