Question
An electron is placed in an electrical field. The magnitude of the electrical field is \( 9 \times 10^{15} \mathrm{~N} \cdot \mathrm{C}^{-1} \) Calculate the magnitude of the force on the electron.
Ask by Nunez Huff. in South Africa
Mar 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The force on the electron is \( 1.44 \times 10^{-3} \, \text{N} \).
Solution
1. The force on a charge in an electric field is given by
\[
F = qE.
\]
2. For an electron, the magnitude of the charge is
\[
|q| = 1.6 \times 10^{-19} \, \text{C}.
\]
3. Substitute the given electric field value \( E = 9 \times 10^{15} \, \text{N} \cdot \text{C}^{-1} \) into the formula:
\[
F = (1.6 \times 10^{-19} \, \text{C})(9 \times 10^{15} \, \text{N/C}).
\]
4. Multiply the numerical values and add the exponents:
\[
1.6 \times 9 = 14.4,
\]
\[
10^{-19} \times 10^{15} = 10^{-4}.
\]
Thus,
\[
F = 14.4 \times 10^{-4} \, \text{N}.
\]
5. Express the force in standard scientific notation:
\[
F = 1.44 \times 10^{-3} \, \text{N}.
\]
The magnitude of the force on the electron is \( 1.44 \times 10^{-3} \, \text{N} \).
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Simplify this solution Mind Expander
To find the magnitude of the force on the electron in an electric field, we can use the formula \( F = qE \), where \( F \) is the force, \( q \) is the charge of the electron, and \( E \) is the electric field strength. The charge of an electron is approximately \( -1.6 \times 10^{-19} \mathrm{~C} \). Given the electric field strength \( E = 9 \times 10^{15} \mathrm{~N/C} \), we calculate: \[ F = qE = (-1.6 \times 10^{-19} \mathrm{~C})(9 \times 10^{15} \mathrm{~N/C}) = -1.44 \times 10^{-3} \mathrm{~N} \] The magnitude of the force is \( 1.44 \times 10^{-3} \mathrm{~N} \). The negative sign indicates that the force acts in the opposite direction of the electric field.
