If the distance between two charges is halved, the electrical force between them increases by a factor 4.
In fact, the magnitude of the electric force between two charges is given by:
![F= k \frac{q_1 q_2}{r^2}](https://tex.z-dn.net/?f=F%3D%20k%20%5Cfrac%7Bq_1%20q_2%7D%7Br%5E2%7D%20)
where
k is the Coulomb's constant
q1 and q2 are the two charges
r is the separation between the two charges
We see that the magnitude of the force F is inversely proportional to the square of the distance r. Therefore, if the radius is halved:
![r'= \frac{r}{2}](https://tex.z-dn.net/?f=r%27%3D%20%5Cfrac%7Br%7D%7B2%7D%20)
the magnitude of the force changes as follows:
![F'=k \frac{q_1 q_2}{r'^2}=k \frac{q_1 q_2}{( \frac{r}{2})^2 }=k \frac{q_1 q_2}{ \frac{r^2}{4} } =4k \frac{q_1 q_2}{r^2}=4 F](https://tex.z-dn.net/?f=F%27%3Dk%20%5Cfrac%7Bq_1%20q_2%7D%7Br%27%5E2%7D%3Dk%20%5Cfrac%7Bq_1%20q_2%7D%7B%28%20%5Cfrac%7Br%7D%7B2%7D%29%5E2%20%7D%3Dk%20%5Cfrac%7Bq_1%20q_2%7D%7B%20%5Cfrac%7Br%5E2%7D%7B4%7D%20%7D%20%3D4k%20%20%5Cfrac%7Bq_1%20q_2%7D%7Br%5E2%7D%3D4%20F%20%20%20)
so, the force increases by a factor 4.
<u>Answer :</u>
(a) d = 0.25 m
(b) d = 0.5 m
<u>Explanation :</u>
It is given that,
Frequency of sound waves, f = 686 Hz
Speed of sound wave at
is, v = 343 m/s
(1) Perfectly destructive interference occurs when the path difference is half integral multiple of wavelength i.e.
........(1)
Velocity of sound wave is given by :
![v=f\times \lambda](https://tex.z-dn.net/?f=v%3Df%5Ctimes%20%5Clambda)
![d=\dfrac{v}{2f}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7Bv%7D%7B2f%7D)
![d=\dfrac{343\ m/s}{2\times 686\ Hz}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7B343%5C%20m%2Fs%7D%7B2%5Ctimes%20686%5C%20Hz%7D)
![d=0.25\ m](https://tex.z-dn.net/?f=d%3D0.25%5C%20m)
Hence, when the speakers are in phase the smallest distance between the speakers for which the interference of the sound waves is perfectly destructive is 0.25 m.
(2) For constructive interference, the path difference is integral multiple of wavelengths i.e.
( n = integers )
Let n = 1
So, ![d=\dfrac{v}{f}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7Bv%7D%7Bf%7D)
![d=\dfrac{343\ m/s}{686\ Hz}](https://tex.z-dn.net/?f=d%3D%5Cdfrac%7B343%5C%20m%2Fs%7D%7B686%5C%20Hz%7D)
![d=0.5\ m](https://tex.z-dn.net/?f=d%3D0.5%5C%20m)
Hence, the smallest distance between the speakers for which the interference of the sound waves is maximum constructive is 0.5 m.
Kinetic energy is never negative, but potential energy can be.
Potential energy depends on height above some reference level,
and you can pick any level you want as the reference. So, if the
object is below the reference level you pick, then its potential
energy relative to your reference level is negative.
What that means is: You have to lift it / do work on it / give it more
energy than it has now ... in order to move it to the reference level.
(That's exactly the situation with electrons bound to an atom. Their
energy is considered negative, because we have to do work and
give them more energy to rip them away from the atom.)
_____________________________________
Regarding the other choices:
-- Kinetic energy is scalar ... Yes. So is potential energy.
-- Kinetic energy increases with height ...
No. It doesn't, but potential energy does.
-- Kinetic energy depends on position ...
No. It doesn't, but potential energy does.
Answer:
As velocity is uniform then acceleration will be zero.
Explanation:
Incomplete question.The complete question is attached below as screenshot along with figure
Answer:
![F=6.00*10^{-6}N](https://tex.z-dn.net/?f=F%3D6.00%2A10%5E%7B-6%7DN)
Force is repulsive
Explanation:
Given data
Current I₁=5.00A
Current I₂=2.00A
Length L=1.20 m
Radius r=0.400m
To find
Force F
Solution
As the force is repulsive because currents are in opposite direction
From repulsive force we know that:
![F=\frac{u_{o}I_{1}I_{2}L}{2\pi r}](https://tex.z-dn.net/?f=F%3D%5Cfrac%7Bu_%7Bo%7DI_%7B1%7DI_%7B2%7DL%7D%7B2%5Cpi%20r%7D)
Substitute the given values