# Answer correct magnitude and direction of electric

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ANSWER: Correct Magnitude and Direction of Electric Fields A small object A, electrically charged, creates an electric field. At a point P located 0.250 directly north of A, the field has a value of 40.0 directed to the south. Part A What is the charge of object A? Hint 1. How to approach the problem Recall that the electric field at a point P due to a point charge is proportional to the magnitude of the charge and inversely proportional to the square of the distance of P from the charge. Furthermore, the direction of the field is determined by the sign of the charge. Hint 2. Find an expression for the charge Which of the following expressions gives the correct magnitude of charge that produces an electric field of magnitude at a distance from the charge? In the following expressions is a constant that has units of . It is strongly repelled. It is strongly attracted. It is weakly attracted. It is weakly repelled. It is neither attracted nor repelled. m N/C q E r k N ⋅ / m 2 C 2

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Hint 1. Magnitude of the electric field of a point charge Given a point charge , the magnitude of the electric field at a distance from the charge is given by , where the constant of proportionality is = 8.99×10 9 . ANSWER: Hint 3. Find the sign of the charge What is the sign of the charge that produces an electric field that points toward the charge? ANSWER: ANSWER: Correct Part B q E r E = k | q | r 2 k N ⋅ / m 2 C 2 q = k E d 2 q = kEd 2 q = k d 2 E q = Ed 2 k positive negative 1.11×10 −9 −1.11×10 −9 2.78×10 −10 −2.78×10 −10 5.75×10 12 −5.75×10 12 C C C C C C
If a second object B with the same charge as A is placed at 0.250 south of A (so that objects A and B and point P follow a straight line), what is the magnitude of the total electric field produced by the two objects at P ? Hint 1. How to approach the problem Since the electric field is a vector quantity, you need to apply the principle of superposition to find the total field at P. The principle of superposition in terms of electric fields says that the total electric field at any point due to two or more charges is the vector sum of the fields that would be produced at that point by the individual charges. Hint 2. Find the vector sum of the electric fields Which of the following diagrams, where and are the electric fields produced by A and B, respectively, correctly represents the situation described in this problem? ANSWER: Hint 3. Find the electric field produced by B at P What is the magnitude of the electric field produced by the second object B at point P? Express your answer in newtons per coulomb. Hint 1. Magnitude of the electric field of a point charge Given a point charge , the magnitude of the electric field at a distance from the charge is given by , m E PA E PB A B C D E 2 q E r E = k | q | r 2

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where the constant of proportionality is = 8.99×10 9 .
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