Concept explainers
(a)
The magnitude and direction of the electric field.
(a)
Answer to Problem 45P
The components of the resultant electric field are
The magnitude of the resultant electric field
Explanation of Solution
Introduction:
Electric field,
Also, two similar charges repel each other and opposite charges attract each other with equal and opposite force.
A charge
Figure 1: Two charges q1 and q2 are placed at the given co-ordinates, and the electric fieldis to be determined due to thetwo given charges is to be found at point P.
Now at point A, the positive charge
The distance between points A and B is
The distance between points P and B is
The distance between points P and A is
Figure 2: The field lines due the two charges at point P and the resultant of the field.
Electric field at distance r from a charge q is given by
Cosine law is used to find the angle
Putting the values from equation, we get
Now, to find the resultant angle, just focus on the filed lines shown in Figure 3.
Figure 3: The resultant field
Now the using the parallelogram theorem, we can find the resultant of the field
and
The resultant angle is calculated as below:
In order to find the angle of resultant electric field, trigonometry is used as shown in Figure 4:
Figure 4: The angle of resultant electric field with the x axis
The angle of the
Thus, the
Conclusion:
The components of the resultant electric field is
The magnitude of the resultant electric field
(b)
The magnitude and direction of the force of the proton.
(b)
Answer to Problem 45P
The components of the resultant force is :
The magnitude of the resultant force is
Explanation of Solution
Introduction:
The electric force between two charges
Also, two similar charges repel each other and opposite charges attract each other with equal and opposite force.
A charge
There is an attractive force on the proton due to charge
Figure 5: Forces acting on the proton placed at point P
The resultant force acting on the proton will be:
The direction of the force will be the same as of the field calculated in the previous section.
Conclusion:
The components of the resultant force is :
The magnitude of the resultant force is
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Chapter 21 Solutions
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