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Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.?
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Four identical charges (q = 50 uC) are placed at the four corners of ...
Problem: Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest when four identical charges are placed at the four corners of a rectangle.
Given:
- Four identical charges (q = 50 uC)
- The rectangle's measurement is 50 x 10-2 m x 75 x 10-2 m
Solution:
To find the magnitude and direction of the resultant force acting on any one of the charges due to the rest, we need to follow these steps:
Step 1: Calculate the distance between each charge and the charge we want to find the resultant force on.
- The distance between the charges on the adjacent corner is d1 = sqrt((0.5 m)^2 + (0.75 m)^2) = 0.895 m
- The distance between the charges on the opposite corner is d2 = sqrt((0.75 m)^2 + (0.5 m)^2) = 0.895 m
Step 2: Calculate the electric force between the charges using Coulomb's law.
- The electric force between the charges on the adjacent corner is F1 = (9 x 10^9 Nm^2/C^2) * ((50 uC)^2) / (0.895 m)^2 = 1.65 N
- The electric force between the charges on the opposite corner is F2 = (9 x 10^9 Nm^2/C^2) * ((50 uC)^2) / (0.895 m)^2 = 1.65 N
Step 3: Calculate the horizontal and vertical components of the force acting on the charge we want to find the resultant force on.
- The horizontal component of the force is Fhor = 2F1 = 3.30 N
- The vertical component of the force is Fver = 2F2 = 3.30 N
Step 4: Calculate the magnitude and direction of the resultant force.
- The magnitude of the resultant force is Fres = sqrt((Fhor)^2 + (Fver)^2) = 4.67 N
- The direction of the resultant force is theta = tan^-1(Fver / Fhor) = 45 degrees
Answer: The magnitude of the resultant force acting on any one of the charges due to the rest is 4.67 N, and the direction is 45 degrees.
Given:
- Four identical charges (q = 50 uC)
- The rectangle's measurement is 50 x 10-2 m x 75 x 10-2 m
Solution:
To find the magnitude and direction of the resultant force acting on any one of the charges due to the rest, we need to follow these steps:
Step 1: Calculate the distance between each charge and the charge we want to find the resultant force on.
- The distance between the charges on the adjacent corner is d1 = sqrt((0.5 m)^2 + (0.75 m)^2) = 0.895 m
- The distance between the charges on the opposite corner is d2 = sqrt((0.75 m)^2 + (0.5 m)^2) = 0.895 m
Step 2: Calculate the electric force between the charges using Coulomb's law.
- The electric force between the charges on the adjacent corner is F1 = (9 x 10^9 Nm^2/C^2) * ((50 uC)^2) / (0.895 m)^2 = 1.65 N
- The electric force between the charges on the opposite corner is F2 = (9 x 10^9 Nm^2/C^2) * ((50 uC)^2) / (0.895 m)^2 = 1.65 N
Step 3: Calculate the horizontal and vertical components of the force acting on the charge we want to find the resultant force on.
- The horizontal component of the force is Fhor = 2F1 = 3.30 N
- The vertical component of the force is Fver = 2F2 = 3.30 N
Step 4: Calculate the magnitude and direction of the resultant force.
- The magnitude of the resultant force is Fres = sqrt((Fhor)^2 + (Fver)^2) = 4.67 N
- The direction of the resultant force is theta = tan^-1(Fver / Fhor) = 45 degrees
Answer: The magnitude of the resultant force acting on any one of the charges due to the rest is 4.67 N, and the direction is 45 degrees.
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Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.?
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Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.?.
Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four identical charges (q = 50 uC) are placed at the four corners of a rectangle. The measurement of the rectangle is 50 x 10-2 m x 75 x 10-2 m. Find the magnitude and direction of the resultant force acting on any one of the charges due to the rest.?.
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