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:
The coordinates of the point is (0,0.55).
Explanation:
Given that,
First charge 
at origin
Second charge 
Second charge at point P = (0,1)
We assume that,
The net electric field between the charges is zero at mid point.
Using formula of electric field
Hence, The coordinates of the point is (0,0.55).
Explanation :
Distance is total path travelled by an object during its entire journey. It is a scalar quantity i.e only magnitude.
Displacement is the shortest distance covered by an object. It is basically the change in position of object. It is a vector quantity i.e direction as well as magnitude.
When an object is travelling in a straight line and stops at the end point, then both distance and displacement are same.
When an object is travelling in a straight line and then changes its direction or we can say come backwards then the magnitude of distance and displacement are different.
Answer: Q=5.46 L/s
COP=2.58
Explanation:
Given that
Cp = 4.18 kJ/(kg.C
density = 1 kg/L
Heat rejected Qr= 570 kJ/min
Power in put W= 2.65 KW
From first law of thermodynamics
U = W+ q
q = Heat absorbed
U = internal energy
W = workdone
U = 570 kJ/min = 9.5 KW
9.5 = 2.65 + q
q = 6.85 KW
COP = q/W
COP = 6.58 / 2.65
COP=2.58
Lets take volume flow rate is Q
So mass flow rate of water m = ρ Q
q = m Cp ΔT
6.85 = 1 x Q x 4.18 ( 23-5)
Q=0.091 L/min
Q=5.46 L/s
