Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

A positive charge [tex]\( q_1 \)[/tex] of [tex]\( 5 \, \mu C \)[/tex] is [tex]\( 3 \times 10^{-2} \, m \)[/tex] west of a positive charge [tex]\( q_2 \)[/tex] of [tex]\( 2 \, \mu C \)[/tex].

What is the magnitude and direction of the electrical force [tex]\( F_e \)[/tex] applied by [tex]\( q_1 \)[/tex] on [tex]\( q_2 \)[/tex]?

A. Magnitude: [tex]\( 3 \, N \)[/tex], Direction: East
B. Magnitude: [tex]\( 3 \, N \)[/tex], Direction: West
C. Magnitude: [tex]\( 100 \, N \)[/tex], Direction: East
D. Magnitude: [tex]\( 100 \, N \)[/tex], Direction: West

Sagot :

GinnyAnswer
Certainly! Let's solve the problem step by step.

We are given:

- [tex]\( q_1 = 5 \mu C = 5 \times 10^{-6} \)[/tex] C
- [tex]\( q_2 = 2 \mu C = 2 \times 10^{-6} \)[/tex] C
- The distance between the charges [tex]\( r = 3 \times 10^{-2} \)[/tex] m

We need to find the magnitude and direction of the electrical force [tex]\( F_e \)[/tex] applied by [tex]\( q_1 \)[/tex] on [tex]\( q_2 \)[/tex].

#### Step 1: Use Coulomb's Law
Coulomb's law states that the magnitude of the electrical force between two point charges is given by:
[tex]\[ F_e = k \frac{q_1 q_2}{r^2} \][/tex]
where [tex]\( k \)[/tex] is Coulomb's constant, approximately [tex]\( 8.99 \times 10^9 \)[/tex] N·m²/C².

#### Step 2: Plug in the values
Let's plug in the given values into Coulomb's law formula:
[tex]\[ q_1 = 5 \times 10^{-6} \text{ C} \][/tex]
[tex]\[ q_2 = 2 \times 10^{-6} \text{ C} \][/tex]
[tex]\[ r = 3 \times 10^{-2} \text{ m} \][/tex]
[tex]\[ k = 8.99 \times 10^9 \text{ N·m}^2/\text{C}^2 \][/tex]

[tex]\[ F_e = 8.99 \times 10^9 \times \frac{(5 \times 10^{-6})(2 \times 10^{-6})}{(3 \times 10^{-2})^2} \][/tex]

#### Step 3: Calculate the magnitude
By calculating the above expression, we get:
[tex]\[ F_e = 99.86168652631305 \text{ N} \][/tex]

So, the magnitude of the electrical force [tex]\( F_e \)[/tex] is approximately [tex]\( 100 \text{ N} \)[/tex].

#### Step 4: Determine the direction
Both charges [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are positive. Since like charges repel each other, the force exerted by [tex]\( q_1 \)[/tex] on [tex]\( q_2 \)[/tex] will be directed away from [tex]\( q_1 \)[/tex]. Given that [tex]\( q_1 \)[/tex] is west of [tex]\( q_2 \)[/tex], the force on [tex]\( q_2 \)[/tex] will be directed towards the east.

Thus, the magnitude and direction of the electrical force [tex]\( F_e \)[/tex] applied by [tex]\( q_1 \)[/tex] on [tex]\( q_2 \)[/tex] are:
[tex]\[ \text{Magnitude: } 100 \text{ N} \][/tex]
[tex]\[ \text{Direction: } \text{east} \][/tex]

So, the correct answer is:
[tex]\[ \text{magnitude: } 100 \text{ N} \][/tex]
[tex]\[ \text{direction: } east \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.