Question

the strength of the electric field 0.5 m from a 6 μc charge is ______ n/c. (use ( k = 8.99 \times 10^9 , \text{n} cdot \frac{\text{m}^2}{\text{c}^2} ) and round answer to the nearest whole number.)
○ 215760
○ 539400
○ 697976
○ 512356

Explanation:

Step1: Recall the electric field formula

The formula for the electric field \( E \) due to a point charge \( q \) at a distance \( r \) is \( E = k\frac{q}{r^{2}} \), where \( k = 8.99\times 10^{9}\ N\cdot\frac{m^{2}}{C^{2}} \), \( q \) is the charge, and \( r \) is the distance from the charge.

Step2: Convert the charge to coulombs

The charge \( q = 6\ \mu C \). Since \( 1\ \mu C=1\times 10^{- 6}\ C \), then \( q = 6\times 10^{-6}\ C \). The distance \( r = 0.5\ m \).

Step3: Substitute the values into the formula

Substitute \( k = 8.99\times 10^{9}\), \( q = 6\times 10^{-6}\ C \) and \( r = 0.5\ m \) into the formula \( E=k\frac{q}{r^{2}} \):

\[

$$\begin{align*} E&=8.99\times 10^{9}\times\frac{6\times 10^{-6}}{(0.5)^{2}}\\ &=8.99\times 10^{9}\times\frac{6\times 10^{-6}}{0.25}\\ &=8.99\times 10^{9}\times24\times 10^{-6}\\ &=8.99\times24\times 10^{3}\\ &=215.76\times 10^{3}\\ & = 215760 \end{align*}$$

\]

Answer:

215760