Question

an object with a 5.0 μc charge is accelerating at 0.0050 m/s² due to an electric field. if the object has a mass of 2.0 mg, what is the magnitude of the electric field?

Explanation:

Step1: Find the force on the object

According to Newton's second - law $F = ma$. First, convert the mass to SI units: $m=2.0\ mg = 2.0\times10^{- 6}\ kg$, $a = 0.0050\ m/s^{2}$. Then $F=ma=(2.0\times10^{-6}\ kg)\times(0.0050\ m/s^{2}) = 1\times10^{-8}\ N$.

Step2: Relate force to electric field

The force on a charged object in an electric field is $F = qE$. Convert the charge to SI units: $q = 5.0\ \mu C=5.0\times10^{-6}\ C$. We can solve for $E$: $E=\frac{F}{q}$.

Step3: Calculate the electric - field magnitude

Substitute $F = 1\times10^{-8}\ N$ and $q = 5.0\times10^{-6}\ C$ into the formula $E=\frac{F}{q}=\frac{1\times10^{-8}\ N}{5.0\times10^{-6}\ C}=2\times10^{-3}\ N/C$.

Answer:

$2\times10^{-3}\ N/C$