Suppose you have a dipole that's free to move in any way (including rotate - imagine it floating in space). And there's an objec
t with charge Q a distance r away. That distance r would be much larger than d, the distance between the charges of the dipole, so we draw the dipole small.
1 answer:
Complete Question
The complete question shown on the first uploaded image
Answer:
a)
The force on Q due to dipole is Attractive
b)
The charge Q exerts attractive force on the dipole
c)
Yes from the above parts, force depends on the sign of charge
d)
e)
The magnitude o force decrease by a factor of 8.0 times
Explanation:
The explanation is shown on the second uploaded image
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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 =
So,
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 )
Answer:
Considering first question
Generally the coefficient of performance of the air condition is mathematically represented as
Here is the inside temperature
while is the outside temperature
What this coefficient of performance represent is the amount of heat the air condition can remove with 1 unit of electricity
So it implies that the air condition removes heat with 1 unit of electricity
Now from the question we are told that the rate at which heat enters an air conditioned building is often roughly proportional to the difference in temperature between inside and outside. This can be mathematically represented as
=>
Here k is the constant of proportionality
So
since 1 unit of electricity removes amount of heat
E unit of electricity will remove
So
=>
given that is constant
=>
From this above equation we see that the electricity required(cost of powering and operating the air conditioner) is approximately proportional to the square of the temperature difference.
Considering the second question
Assuming that
and
Hence
Here K stand for a constant
So
=>
Now if the
Then
=>
So from this see that the electricity require (cost of powering and operating the air conditioner)when the inside temperature is low is much higher than the electricity required when the inside temperature is higher
Considering the third question
Now in the case where the heat that enters the building is at a rate proportional to the square-root of the temperature difference between inside and outside
We have that
So
=>
Assuming is a constant
Then
From this above equation we see that the electricity required(cost of powering and operating the air conditioner) is approximately proportional to the square root of the cube of the temperature difference.