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Particle A of charge 3.00 × 10−4 C is at the origin, particle B of charge −6.00 × 10−4 C is at (4.00 m, 0), and particle C of charge 1.00 × 10−4 C is at (0, 3.00 m). We wish to find the net electric force on C. (a) What is the x component of the electric force exerted by A on C? (b) What is the y component of the force exerted by A on C? (c) Find the magnitude of the force exerted by B on C. (d) Calculate the x component of the force exerted by B on C. (e) Calculate the y component of the force exerted by B on C. (f) Sum the two x components from parts (a) and (d) to obtain the resultant x component of the electric force acting on C. (g) Similarly, find the y component of the resultant force vector acting on C. (h) Find the magnitude and direction of the resultant electric force acting on C.
(a)
The
Answer to Problem 23.18P
The
Explanation of Solution
The charge of particle
The diagram for the given condition is shown below.
Figure 1
Write the formula to calculate the electrical force
Here,
The particle
The distance from the
Thus, the
Conclusion:
Therefore, the
(b)
The
Answer to Problem 23.18P
The
Explanation of Solution
Write the formula to calculate the electrical force
Substitute
Conclusion:
Therefore, the
(c)
The magnitude of the force exerted by
Answer to Problem 23.18P
The magnitude of the force exerted by
Explanation of Solution
By Pythagoras theorem, write the expression distance between
Write the formula to calculate the electrical force
Here,
Substitute
Conclusion:
Therefore, the magnitude of the force exerted by
(d)
The
Answer to Problem 23.18P
The
Explanation of Solution
From part (c), the magnitude of the force exerted by
Resolve the side
From Figure I
Here,
Write the formula to calculate the
Here,
Substitute
Conclusion:
Therefore, the
(e)
The
Answer to Problem 23.18P
The
Explanation of Solution
From part (c), the magnitude of the force exerted by
Resolve the side
From Figure I,
Write the formula to calculate the
Here,
Substitute
Conclusion:
Therefore, the
(f)
The resultant
Answer to Problem 23.18P
The resultant
Explanation of Solution
From part (a), the
From part (d), the
Write the formula to calculate the resultant force acting on the particle
Here,
Substitute
Conclusion:
Therefore, the resultant
(g)
The resultant
Answer to Problem 23.18P
The resultant
Explanation of Solution
From part (b), the
From part (e), the
Write the formula to calculate the resultant force acting on the particle
Here,
Substitute
Conclusion:
Therefore, the resultant
(h)
The magnitude and direction of the resultant electric force acting on
Answer to Problem 23.18P
The magnitude and direction of the resultant electric force acting on
Explanation of Solution
From part (g), the resultant
From part (f), the resultant
Write the formula to calculate the resultant force acting on the particle
Here,
Substitute
Write the formula to calculate the direction of the resultant force acting on
Here,
Substitute
The direction of the resultant force is counterclockwise from
Conclusion:
Therefore, the magnitude and direction of the resultant electric force acting on
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