Radius of a Raindrop given Charge and Electric Potential

[freddy13]

Homework Statement

A spherical rain drop carries a charge of 5×10-6 C and has a potential of 8.800×10-8 V at the surface. Find the radius of the drop.

Homework Equations

V = (kQ)/r

The Attempt at a Solution

I simply moved V and r to their respective spots and plugged in my numbers. I got a very large number of 5.11*10^11, so i am wondering if my units are wrong or if I am doing something else wrong. Thanks for your help!

 

[TSny]

Hello, freddy13.

You're right, you're getting a ridiculous answer even though your method is correct. (Your answer for the radius is more than 3 times the distance to the sun.) The value for the potential looks very suspicious. Are you sure that 10 is raised to the negative 8 power? Also, the value for the charge seems very high for a raindrop.

 

[freddy13]

Yeah I copied the problem exactly! It has to be something with the units that I am missing, that seems to be the only possibility!

 

[TSny]

I agree. It must be a misprint in the statement of the problem.

 

[Nickie]

I would first check to make sure that all of the units are consistent. The equation you used, V = (kQ)/r, requires the charge (Q) to be in coulombs (C) and the radius (r) to be in meters (m). The potential (V) should be in volts (V). If your units are not consistent, this could be causing your large result.

Additionally, I would double check the values given in the problem to make sure they are accurate and in the correct units. If everything seems to be correct, I would suggest using a calculator or computer program to double check your calculations and make sure there are no errors.

If you are still getting a large result, it may be helpful to break down the equation and solve for the radius step by step. For example, first solve for kQ, then divide by V, and finally take the square root to find the radius. This can help pinpoint where the error may be occurring.

Overall, it is important to always double check your work and make sure your units are consistent when solving scientific equations.