Question

A single point charge sits alone in a region of space. The electric field due to the charge at a distance of 0.298 meters is 2.46e+3 N/C. Calculate the magnitude of the charge on the point charge.

Answer 1

The magnitude of the charge on the point charge can be found using Coulomb's law. After rearranging the formula and inserting given values, the charge measures approximately 1.96e-8C.

Step-by-step explanation:

The nature of the question hints towards the use of Coulomb's law in Electric Fields. Coulomb's law describes the magnitude of the electric field (E) created by a single point charge (q) at a certain distance (r) in its vicinity, which can be expressed as E = k*q/r^2, where k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2). In this case, we're given E (2.46e+3 N/C) and r (0.298m), and we're asked to find q.

To find the charge, we simply rearrange the formula to solve for q: q = E*r^2/k. Inserting the given values, q = (2.46e+3 N/C) * (0.298 m)^2 / (8.99 x 10^9 Nm^2/C^2). After performing the calculation, the magnitude of the charge on the point charge approximates to 1.96e-8C.

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Answer 2

The magnitude of the charge on the point charge is approximately
`\(2.43 * 10^(-11) \ \text{C}\)`.

To calculate the magnitude of the point charge, we can use Coulomb's law, which states that the electric field
`(\(E\))` created by a point charge
`(\(Q\))` at a distance
`(\(r\))` is given by the equation
`\(E = (kQ)/(r^2)\)`, where
`\(k\)` is Coulomb's constant
`(\(8.99 * 10^9 \ \text{N m}^2/\text{C}^2\))`.

Given that
`\(E = 2.46 * 10^3 \ \text{N/C}\)` and
`\(r = 0.298 \ \text{m}\)`, we can rearrange the equation to solve for
`\(Q\)`:

`\[ Q = (Er^2)/(k) \]`

Substitute the values:

`\[ Q = \frac{(2.46 * 10^3 \ \text{N/C}) * (0.298 \ \text{m})^2}{8.99 * 10^9 \ \text{N m}^2/\text{C}^2} \]`

`\[ Q \approx \frac{2.46 * 10^3 \ \text{N/C} * 0.088804 \ \text{m}^2}{8.99 * 10^9 \ \text{N m}^2/\text{C}^2} \]`

`\[ Q \approx \frac{0.2184544 \ \text{N m/C}}{8.99 * 10^9 \ \text{N m}^2/\text{C}^2} \]`

`\[ Q \approx 2.43 * 10^(-11) \ \text{C} \]`

Therefore, the magnitude of the charge on the point charge is approximately
`\(2.43 * 10^(-11) \ \text{C}\)`.