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Answer:
d=9.462×10^15 meters
Explanation:
<u>Relation between distance, temps and velocity:</u>
d=v*t
t=1year*(365days/1year)*/(24hours/1day)*(3600s/1h)=31536000s
So:
1 light year=d=3*10^8m/s*3.154*10^7s=9.462×10^15 meters
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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 )
-- Multiply each side of the formula by 2
-- Then divide each side by t
-- Then subtract V(i) from each side.