Question

A source charge of 3 µc generates an electric field of 2.86 × 105 n/c at the location of a test charge. what is the distance, to the nearest hundredth, of the test charge from the source charge? k equals 8.99 times 10 superscript 9 baseline n times startfraction meters squared over coulombs squared. m

Answer 1

0.31 m

Step-by-step explanation:

Answer 2

Hello!

Using the equation for the electric field produced by a source charge:

`E = (kq)/(r^2)`

E = Electric Field Strength ( 2.86 × 10⁵ N/C)
k = Coulomb's Constant ( 8.99 × 10⁹ Nm²/C²)

q = Charge of source charge (3 μC = 0.000003 C)

r = distance of test charge from source charge (m²)

We can rearrange the equation to solve for distance to make plugging in values easier. (Isolate for 'r').

`Er^2 = kq\\\\r^2 = (kq)/(E)\\\\r = \sqrt{(kq)/(E)}`

Plug in the given values.

`r = \sqrt{((8.99*10^9)(3*10^(-6)))/((2.86*10^5))} = \boxed{0.307 m}`