What is the strength of the electric field 0.020 m from a $12 \mu C$ charge? (Use $k =8.99 \times 10^{\circ} N \frac{ m ^2}{ c ^2}$)
Answer (1)
Use the formula for the electric field due to a point charge: E = k r 2 ∣ q ∣ .
Substitute the given values: k = 8.99 × 1 0 9 N C 2 m 2 , q = 12 × 1 0 − 6 C , and r = 0.020 m .
Calculate the electric field strength: E = ( 8.99 × 1 0 9 ) ( 0.020 ) 2 12 × 1 0 − 6 = 2.7 × 1 0 8 N / C .
The strength of the electric field is 2.7 × 1 0 8 N / C .
Explanation
Problem Analysis We are asked to find the electric field strength at a distance of 0.020 m from a 12 μ C charge. We are given the value of Coulomb's constant k = 8.99 × 1 0 9 N C 2 m 2 .
Formula Introduction The formula for the electric field strength E due to a point charge q at a distance r is given by:
E = k r 2 ∣ q ∣
where:
E is the electric field strength (in N/C)
k is Coulomb's constant ( 8.99 × 1 0 9 N C 2 m 2 )
q is the magnitude of the charge (in C)
r is the distance from the charge (in m)
Calculation We are given:
q = 12 μ C = 12 × 1 0 − 6 C
r = 0.020 m
k = 8.99 × 1 0 9 N C 2 m 2
Substitute these values into the formula:
E = ( 8.99 × 1 0 9 N C 2 m 2 ) ( 0.020 m ) 2 ∣12 × 1 0 − 6 C ∣
E = ( 8.99 × 1 0 9 ) 0.0004 12 × 1 0 − 6 N / C
E = 0.0004 8.99 × 12 × 1 0 3 N / C
E = 269700000 N / C
E = 2.697 × 1 0 8 N / C
Rounding to two significant figures, we get:
E ≈ 2.7 × 1 0 8 N / C
Final Answer Therefore, the strength of the electric field 0.020 m from a 12 μ C charge is approximately 2.7 × 1 0 8 N / C .
Examples
Understanding electric fields is crucial in many real-world applications. For instance, designing electronic devices like capacitors and transistors requires precise knowledge of how electric fields behave around charges. In medical equipment such as MRI machines, strong and carefully controlled electric fields are used to manipulate charged particles. Moreover, in environmental science, understanding electric fields helps in studying atmospheric phenomena like lightning and designing effective lightning protection systems. By mastering the principles behind electric fields, you gain the ability to engineer safer and more efficient technologies.
