How Much Water Can Lightning Boil Away from a Tree?

[mpm]

I need help with 2 questions that I can't seem to figure out. I had them for homework but I never got it right and the homework has since been turned in.

I was told I would most likely see these problems again on the exam. Therefore I need to learn how to do them. Can anyone help me out on these?

Question 1:

A certain strom cloud has a potential difference of 8.9 x 10^7 V relative to a tree. Water has a specific heat of 4186 J/kg*C, a boiling point of 100 Celsius and a heat of vaporization of 2.26 x 10^6 J/kg.

If, during a lightning storm, 52 C charge is transferred through this potential difference and 1.96% of the netery is absorbed by the tree, how much water (sap in the tree) initially at 20.9 celsius can be boiled away? Answer in kg.


Question 2:

An insulating sphere of radius 14 cm has a uniform charge dnesity through its volume. If the magnitude of the electric field at a distance of 7.5029 cm from the center is 98545.6 N/C, what is the magnitude of the electric field at 28.0078 cm from the center? Answer in N/C. (Radius of sphere is 14 cm)


If anyone can help me I would really appreciate it.

 

[fargoth]

1) this problem is very simplified.. you know that $$E=QV$$ where E is the energy transfered, Q is the charge transferred and V is the voltage difference in which it was tranfered with.

now just calculate how much energy you transferred to that tree and how many kilo's of water you can vaporize with it...

 

[fargoth]

as for the second question:

the field of a uniformly charged sphere is like a point charge at the middle with the net charge...
$$E=\frac{Q}{r^2}$$
you can find the net charge, and calculate the field at the new distance, or just say the ratio between the fields is equal to the square of the ratio between the two radii.. $$\frac{E_1}{E_2}=(\frac{r_2}{r_1})^2$$