Concept explainers
Three charged particles are aligned along the x axis as shown in Figure P22.35. Find the electric field at (a) the position (2.00 m, 0) and (b) the position (0, 2.00 m).
Figure P22.35
(a)
The electric field at the position
Answer to Problem 35AP
The electric field at the position
Explanation of Solution
Given Info: Three charges are acting on the same line along the
According to Coulomb’s law, the electric field created by a charge
Here,
The electric field at a point due to number of charges is resultant of the electric field due to the individual charges.
The figure for the position of point charges is shown below.
Figure (1)
The electric field due to charge
Here,
Substitute
The electric field due to charge
Here,
Substitute
The electric field due to charge
Here,
Substitute
The resultant electric field can be given as,
Here,
Substitute
Thus, the electric field at position
Conclusion:
Therefore, the electric field at the position
(b)
The electric field at the position
Answer to Problem 35AP
The electric field at the position
Explanation of Solution
Given Info: Three charges are acting on the same line along the
The figure for the position of point charges is shown below,
Figure (2)
According to Pythagoras theorem, the distance between the charge
Here,
According to Pythagoras theorem, the distance between the charge
Here,
The electric field due to charge
Here,
Substitute
In component form the electric field can be written as,
According to right angle triangle property,
And,
Substitute
The electric field due to charge
Here,
Substitute
The electric field due to charge
Here,
Substitute
In component form the electric field can be written as,
According to right angle triangle property,
And,
Substitute
The resultant electric field can be given as,
Here,
Substitute
Thus, the electric field at position
Conclusion:
Therefore, the electric field at position
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