Alan leaves Los Angeles at 8:00 A.M. to drive to San Francisco 400 mi away. He manages to travel at a steady 50 mph in spite of
1 answer:
Answer:
a) Beth will reach before Alan
b)Beth has to wait 20 min for Alan to arrive
Explanation:
let 'd' be distance b/w Los Angeles and San Francisco i.e 400 mi
considering ,
Alan's speed =50mph
Beth's speed =60mph
->For Alan:
The time required = d/
= 400/50 => 8h
-> For beth:
The time required => 6h 40m
Alan will reach at 8:00 a.m +8h = 4:00p.m.
Beth will reach at 9:00 a.m +6h 40m= 3:40p.m.
a) Beth will reach before Alan
b)Beth has to wait 20 min for Alan to arrive
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1) Electric potential inside the sphere:
2) Ratio Vcenter/Vsurface: 3/2
3) Find graph in attachment
Explanation:
1)
The electric field inside the sphere is given by
where
is the vacuum permittivity
Q is the charge on the sphere
R is the radius of the sphere
r is the distance from the centre at which we compute the field
For a radial field,
Therefore, we can find the potential at distance r by integrating the expression for the electric field. Calculating the difference between the potential at r and the potential at R,
The potential at the surface, V(R), is that of a point charge, so
Therefore we can find the potential inside the sphere, V(r):
2)
At the center,
r = 0
Therefore the potential at the center of the sphere is:
On the other hand, the potential at the surface is
Therefore, the ratio V(center)/V(surface) is:
3)
The graph of V versus r can be found in attachment.
We observe the following:
- At r = 0, the value of the potential is , as found in part b) (where
)
- Between r and R, the potential decreases as
- Then at r = R, the potential is
- Between r = R and r = 3R, the potential decreases as , therefore when the distance is tripled (r=3R), the potential as decreased to 1/3 (
)
Learn more about electric fields and potential:
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