Multiple Choice
What is the direction of the net force on the charge at the center of the square in the following figure?
24. Electric Force & Field; Gauss' Law
Coulomb's Law (Electric Force)
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A charge is at the origin, acharge is at. Where, on the x-axis, could you place a charge so that it would experience no net force?
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Verified step by step guidance1
Identify the charges and their positions: A 3.0 nC charge is at the origin (x=0 cm), a -12 nC charge is at x=2.0 cm, and we need to find the position for a -45 nC charge where it experiences no net force.
Understand that the net force on the -45 nC charge will be zero when the forces due to the 3.0 nC charge and the -12 nC charge cancel each other out. This means the magnitudes of the forces must be equal and opposite.
Use Coulomb's Law to express the force between two point charges: F = k * |q1 * q2| / r^2, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
Set up the equation for the forces: The force due to the 3.0 nC charge on the -45 nC charge should equal the force due to the -12 nC charge on the -45 nC charge. Let the position of the -45 nC charge be x cm. The distance from the 3.0 nC charge is |x| cm, and from the -12 nC charge is |x - 2| cm.
Solve the equation: k * |3.0 nC * -45 nC| / x^2 = k * |-12 nC * -45 nC| / (x - 2)^2. Simplify and solve for x to find the position where the net force is zero.
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