answer.
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
horrorfan
17 days ago
10

A uniformly charged spherical droplet of mercury has electric potential Vbig throughout the droplet. The droplet then breaks int

o n identical spherical droplets, each of which has electric potential Vsmall throughout its volume. The n small droplets are far enough apart from one another that they do not interact significantly.
Find (Vbig)/(Vsmall) , the ratio of Vbig, the electric potential of the initial drop, to Vsmallthe electric potential of one of the smaller drops.(The ratio should be dimensionless and should depend only on n)
Physics
1 answer:
kicyunya [2.2K]17 days ago
7 0

Answer:

\frac{V_{big}}{V_{small}} = n^{2/3}

Explanation:

Let the charge on the large droplet be denoted as Q.

When the radius of the droplet is R, the electric potential for the larger droplet can be expressed as:

V_{big} = \frac{KQ}{R}

If it splits into n identical droplets, let the charge of each be "q" and their radius be "r".

Applying volume conservation gives us:

\frac{4}{3}\pi R^3 = n(\frac{4}{3}\pi r^3)

r = \frac{R}{n^{1/3}}

Now, the potential for the smaller droplets is given as:

V_{small} = \frac{kq}{r}

V_{small} = \frac{K(Q/n)}{\frac{R}{n^{1/3}}}

V_{small} = \frac{1}{n^{2/3}}\frac{KQ}{R}

\frac{V_{big}}{V_{small}} = n^{2/3}

You might be interested in
An aluminum wire of length 1.0 meter has a resistance of 9.0x10^-3 ohm. If the wire were cut into two equal lengths, each length
Sav [2217]

Answer: since resistance is influenced by length, the resistance will be equally distributed as the wire is cut into two equal parts, resulting in

4.5 * 10^-3 ohm.

Explanation:

0 0
1 month ago
Read 2 more answers
A fire hose held near the ground shoots water at a speed of 6.5 m/s. At what angle(s) should the nozzle point in order that the
inna [2205]
The velocity of water can be decomposed into its vertical and horizontal components:
v_x = 6.5 cos \theta \\ v_y = 6.5 sin \theta

The vertical component will exhibit a parabolic trajectory due to gravity, while the horizontal component will be linear:
y(t) = -4.9t^2 + (6.5sin \theta) t \\ \\ x(t) = (6.5 cos \theta) t
To determine when the water reaches the ground 2.5m away, set y= 0 and x = 2.5
-4.9t^2 + (6.5sin \theta) t=0 \\ \\ t = \frac{6.5}{4.9} sin \theta \\ \\(6.5 cos \theta)(\frac{6.5}{4.9} sin \theta) = 2.5 \\ \\ sin \theta cos \theta = 0.29 \\ \\ sin 2\theta = 0.58 \\ \\ 2\theta = 35.4, 144.6 \\ \\ \theta = 17.7,72.3
8 0
11 days ago
A 1.0 kg brick falls off a ledge of height 44m and lands on the ground at 3.0 s later.
Keith_Richards [2256]
vf^2 = 2ad
vf^2 = 2(9.81)(44m)
vf^2 = 863.28
vf = √863.28
vf = 29.4  - using equations of motion

ME = PE + KE
ME = mgh + 1/2mv^2
ME = (1)(9.81)(44) + 1/2(1)(3^2)
ME = 431.64 + 4.5
ME = 436.14 - applying the principle of energy conservation

hope this helps:)
7 0
2 days ago
A rod 12.0 cm long is uniformly charged and has a total charge of -20.0 µc. determine the magnitude and direction of the electri
Ostrovityanka [2204]
<span>Let Q be the charge, thus Q = -20.0 µC.</span>
Define D as the distance between the center of the rod and the specified point. Therefore,
D=0.32 - 0.12 = 0.2 m
<span>L = 0.12 m, which represents the length of the rod
</span><span>To find the magnitude and direction of the electric field along the axis of the rod at a point 32.0 cm from its center, use the formula:
</span><span>E = K·Q/r²
</span>or<span>E = kQ/D(D+L), where k</span> is a constant equal to 8.99 x 10<span>9</span> N m
2/C2.<span>Consequently,[TAG_21]]E=(</span>8.99 x 109 N m2/C2.* (-20.0 µC))/(<span>0.2 m*0.32m)</span><span>

</span>
7 0
2 days ago
Read 2 more answers
How many electrons must be removed from a neutral, isolated conducting sphere to give it a positive charge of 8.0 x 10 8 C? [Q=n
inna [2205]

The new charge of the ball will amount to 8x10^8C after removing 5x10^27 electrons.

Explanation:

Initially, if the sphere is electrically neutral, its charge stands at 0C.

When an electron with a charge of (-1.6*10^-19 C) is taken away, we effectively add a positive charge, leading to:

1.6*10^-19 C as the sphere's new charge.

For a total of N electrons removed, the sphere's overall charge now becomes:

N*1.6*10^-19 C.

To calculate N when:

N*1.6*10^-19 C = 8.0x 10^8 C.

We find that N is: (8.0/1.6)x10^(8 + 19) = 5x10^27 electrons.

7 0
1 month ago
Other questions:
  • A weatherman carried an aneroid barometer from the ground floor to his office atop the Sears Tower in Chicago. On the level grou
    10·1 answer
  • A 2600-m-high mountain is located on the equator. how much faster does a climber on top of the mountain move than a surfer at a
    14·1 answer
  • A 96-mH solenoid inductor is wound on a form 0.80 m in length and 0.10 m in diameter. A coil is tightly wound around the solenoi
    12·1 answer
  • Object A and object B are initially uncharged and are separated by a distance of 1 meter. Suppose 10,000 electrons are removed f
    11·1 answer
  • A popcorn-maker transfers 250 J of energy into other energy stores every second. What is its power?
    9·1 answer
  • An isolated charged point particle produces an electric field with magnitude E at a point 2 m away. At a point 1 m from the part
    7·1 answer
  • An overhang hollow shaft carries a 900 mm diameter pulley, whose centre is 250 mm from the centre of the nearest bearing. The we
    10·1 answer
  • All forces on the bullets cancel so that the net force on a bullet is zero, which means the bullet has zero acceleration and is
    5·2 answers
  • When you’re driving on a level road and there’s ice on the pavement, you hardly notice that ice while you’re heading straight at
    12·1 answer
  • An airplane cruises at 850 km/h relative to the air. It is flying from Denver, Colorado, due west to Reno, Nevada, a distance of
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!