Question

One issue encountered during the exploration of Mars has been the accumulation of static charge on land-roving vehicles, resulting in a potential of \(100 .\) V or more. Calculate how much charge must be placed on the surface of a sphere of radius \(1.00 \mathrm{~m}\) for the electric potential just above the surface to be \(100 .\) V. Assume that the charge is uniformly distributed.

Short answer

Answer: The required charge is approximately \(1.11×10^{-8}\) Coulombs.

Step-by-step solution

Write down the given information

We are given: - Electric potential (V): 100 V - Radius of the sphere (r): 1.00 m

Write down the formula for electric potential

The formula for electric potential due to a point charge is: $$V = \frac{kQ}{r}$$

Rearrange the formula to find Q

To find the charge on the sphere (Q), we need to isolate it in the formula. We can do this by multiplying both sides by r and dividing both sides by k: $$Q = \frac{V * r}{k}$$

Substitute the given values

Now, we can plug in the given values of V and r, and the constant value of k: $$Q = \frac{100 * 1.00}{8.99×10^9}$$

Calculate Q

Now, we can calculate the value of Q: $$Q = \frac{100}{8.99×10^9} = 1.11×10^{-8} \mathrm{C}$$ The required charge to create an electric potential of 100 V just above the surface of the sphere is approximately \(1.11×10^{-8}\) Coulombs.