Coulomb's law for the magnitude of the force F𝐹 between two particles with charges Q𝑄 and Q′𝑄′ separated by a distance d𝑑 is|F|=K|QQ′|d2|𝐹|=𝐾|𝑄𝑄′|𝑑2,where K=14πϵ0𝐾=14𝜋𝜖0, and ϵ0=8.854×10−12C2/(N⋅m2)𝜖0=8.854×10−12C2/(N⋅m2) is the permittivity of free space.Consider two point charges located on the x axis: one charge, q1𝑞1 = -19.5 nCnC , is located at x1𝑥1 = -1.690 mm ; the second charge, q2𝑞2 = 31.0 nCnC , is at the origin (x𝑥 = 0).Part AWhat is (Fnet3)x(𝐹net3)𝑥 , the x-component of the net force exerted by these two charges on a third charge q3𝑞3 = 48.5 nCnC placed between q1𝑞1 and q2𝑞2 at x3𝑥3 = -1.185 mm ?Your answer may be positive or negative, depending on the direction of the force.Express your answer numerically in newtons to three significant figures.View Available Hint(s)
Question
Coulomb's law for the magnitude of the force F𝐹 between two particles with charges Q𝑄 and Q′𝑄′ separated by a distance d𝑑 is|F|=K|QQ′|d2|𝐹|=𝐾|𝑄𝑄′|𝑑2,where K=14πϵ0𝐾=14𝜋𝜖0, and ϵ0=8.854×10−12C2/(N⋅m2)𝜖0=8.854×10−12C2/(N⋅m2) is the permittivity of free space.Consider two point charges located on the x axis: one charge, q1𝑞1 = -19.5 nCnC , is located at x1𝑥1 = -1.690 mm ; the second charge, q2𝑞2 = 31.0 nCnC , is at the origin (x𝑥 = 0).Part AWhat is (Fnet3)x(𝐹net3)𝑥 , the x-component of the net force exerted by these two charges on a third charge q3𝑞3 = 48.5 nCnC placed between q1𝑞1 and q2𝑞2 at x3𝑥3 = -1.185 mm ?Your answer may be positive or negative, depending on the direction of the force.Express your answer numerically in newtons to three significant figures.View Available Hint(s)
Solution
To solve this problem, we need to calculate the force exerted on q3 by both q1 and q2, and then add these forces together to get the net force.
Step 1: Convert all quantities to SI units.
q1 = -19.5 nC = -19.5 * 10^-9 C q2 = 31.0 nC = 31.0 * 10^-9 C q3 = 48.5 nC = 48.5 * 10^-9 C x1 = -1.690 mm = -1.690 * 10^-3 m x3 = -1.185 mm = -1.185 * 10^-3 m
Step 2: Calculate the distance between each pair of charges.
d13 = x1 - x3 = -1.690 * 10^-3 m - (-1.185 * 10^-3 m) = -0.505 * 10^-3 m d23 = x3 = -1.185 * 10^-3 m
Step 3: Calculate the force exerted on q3 by q1 and q2 using Coulomb's law.
F13 = K * |q1q3| / d13^2 = (9 * 10^9 Nm^2/C^2) * |-19.5 * 10^-9 C * 48.5 * 10^-9 C| / (-0.505 * 10^-3 m)^2 F23 = K * |q2q3| / d23^2 = (9 * 10^9 Nm^2/C^2) * |31.0 * 10^-9 C * 48.5 * 10^-9 C| / (-1.185 * 10^-3 m)^2
Step 4: Add the forces together to get the net force.
Fnet3 = F13 + F23
Note: The direction of the force is determined by the sign of the charges. If the product of the charges is positive, the force is repulsive and if the product is negative, the force is attractive. In this case, F13 is attractive (negative) and F23 is repulsive (positive).
Finally, calculate the values of F13, F23 and Fnet3 and express your answer in newtons to three significant figures.
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Coulomb's Law
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