The electric force generated by two point charges separated by Distance A is 4 times greater than the electric force generated when separated by Distance B. How does Distance A compare to Distance B?A.Distance A is longer by a factor of 2.B.Distance A is longer by a factor of 4.C.Distance A is shorter by a factor of 2.D.Distance A is shorter by a factor of 4.
Question
The electric force generated by two point charges separated by Distance A is 4 times greater than the electric force generated when separated by Distance B. How does Distance A compare to Distance B?A.Distance A is longer by a factor of 2.B.Distance A is longer by a factor of 4.C.Distance A is shorter by a factor of 2.D.Distance A is shorter by a factor of 4.
Solution
The electric force between two charges is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, this is expressed as F = kq1q2/r^2, where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance.
Given that the force when the charges are separated by Distance A is 4 times greater than when they are separated by Distance B, we can set up the following equation:
F_A = 4*F_B
Substituting Coulomb's Law into this equation gives us:
kq1q2/A^2 = 4kq1*q2/B^2
Solving for A gives us:
A = B/√4
Therefore, Distance A is shorter by a factor of 2 compared to Distance B. So, the correct answer is C. Distance A is shorter by a factor of 2.
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