Question

What is the force exerted on an electron by a point charge of +0.7 micro coulomb when they are 5mm apart?​

Answer 1

The force exerted on an electron by a point charge can be calculated using Coulomb's Law, which involves the charge values and the distance between them, converted to meters. By substituting the values into the Coulomb's Law formula, we obtain the force in newtons.

Step-by-step explanation:

The force exerted on an electron by a point charge can be calculated using Coulomb's Law, which states that the force (F) between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance (r) between them.

First, we need to convert the distance from millimeters to meters:

• 5 mm = 0.005 m

Now we apply Coulomb's Law, F = k |q1 * q2| / r^2, where:

• k is Coulomb's constant (approx. 8.99 x 10^9 Nm^2/C^2)
• q1 is the charge of the point charge (+0.7 μC = +0.7 x 10^-6 C)
• q2 is the charge of the electron (-1.6 x 10^-19 C, the charge of the electron is known and constant)

Substituting the given values into the formula:

F = k |(+0.7 x 10^-6 C) * (-1.6 x 10^-19 C)| / (0.005 m)^2

This will give us the magnitude of the force in newtons (N).

The sign will be negative, indicating an attractive force since the charges are opposite in sign (positive and negative).

Answer 2

Approximately
`4.0* 10^(-11)\; {\rm N}`, in the direction pointing towards the point charge.

Step-by-step explanation:

By Coulomb's Law, the magnitude of the electrostatic force between two point charges is:

`\displaystyle F = (k\, q_(1)\, q_(2))/(r^(2))`,

Where:

• 
  `k \approx 8.99 * 10^(9)\; {\rm N\cdot m^(2)\cdot C^(-2)}` is the Coulomb constant,
• 
  `q_(1)` and
  `q_(2)` are the magnitudes of the two point charges, and
• 
  `r` is the distance between the two point charges.

The magnitude of the charge on an electron is known as the elementary charge: approximately
`1.602 * 10^(-19)\; {\rm C}`.

Apply unit conversion and ensure that all other quantities are measured in standard units: Coulomb for charge, and meters for distance.

• Magnitude of the point charge:
  
  `\begin{aligned} q_(1) &= 0.7\; {\rm \mu C} \\ &= 0.7\; {\rm \mu C}* \frac{1\; {\rm C}}{10^(6)\; {\rm \mu C}} \\ &= 0.7 * 10^(-6)\; {\rm C} \end{aligned}`.
• Distance between the two charges:
  
  `\begin{aligned} d &=5\; {\rm mm} \\ &= 5\; {\rm mm}* \frac{1\; {\rm m}}{10^(3)\; {\rm mm}} \\ &= 5.0 * 10^(-3)\; {\rm m} \end{aligned}`.

The electron can also be considered as a point charge given that its radius is much smaller than the distance between the two charges. Hence, by Coulomb's Law, the magnitude of the electrostatic force between the two charges would be:

`\begin{aligned} F &= (k\, q_(1)\, q_(2))/(r^(2)) \\ &= ((8.99 * 10^(9))\, (0.7 * 10^(-6))\, (1.602 * 10^(-19)))/((5* 10^(-3))^(2)) \; {\rm N} \\ &\approx 4.0 * 10^(-11)\; {\rm N}\end{aligned}`.

Two point charges repel each other if they are of the same sign, and attract each other if they are of opposite signs. The charge on an electron is negative, whereas the
`\!0.7\;{\rm \mu C}` point charge is positive. Hence, the two charges would attract each other, and the force exerted on the electron would point towards the
`0.7\;{\rm \mu C}` point charge.