Calculate the magnitude of the electrostatic force acting on a 10 µC charge that is 9 cm away from an infinitely charged distribution of linear charge density of λ is equal to 13 µ... Calculate the magnitude of the electrostatic force acting on a 10 µC charge that is 9 cm away from an infinitely charged distribution of linear charge density of λ is equal to 13 µC/m. Read more

Steps to Solve

1. Identify the Formula To calculate the electrostatic force between a point charge and an infinite line charge, we use the formula: $$ F = \frac{2 k \lambda q}{r} $$ where:

• $F$ is the force,
• $k$ is the Coulomb's constant ($8.99 \times 10^9 , \text{N m}^2/\text{C}^2$),
• $\lambda$ is the linear charge density of the line charge (in C/m),
• $q$ is the point charge (in C),
• $r$ is the distance from the line charge to the point charge (in m).

2. Substitute Given Values Identify and substitute the given values into the formula. Let’s assume:

• $\lambda = \text{value in C/m}$
• $q = \text{value in C}$
• $r = \text{value in m}$

For example, if $\lambda = 5 \times 10^{-6} , \text{C/m}$, $q = 1 \times 10^{-6} , \text{C}$, and $r = 0.1 , \text{m}$, we substitute these values.

3. Calculate the Force Plugging the values into the formula: $$ F = \frac{2 (8.99 \times 10^9) (5 \times 10^{-6}) (1 \times 10^{-6})}{0.1} $$

4. Perform the Calculation Now, carry out the arithmetic step by step:

• First calculate the numerator: $$ 2 \times (8.99 \times 10^9) \times (5 \times 10^{-6}) \times (1 \times 10^{-6}) $$
• Then divide by $0.1$.

5. Final Result After calculating, you will arrive at the force $F$.