A single point charge is located at an unknown point on the x-axis. There are no

Question

A single point charge is located at an unknown point on the x-axis. There are no other charged objects nearby. You measure the electric field at x = +2.0 m to be 5200 N/C, directed in the +x direction, while the field at x = +5.0 m has a magnitude of 1300 N/C. What is the sign and magnitude of the point charge?

There are two possible solutions. First, we'll do the solution in which the charge on the point charge has the larger magnitude. For this solution, the sign and magnitude of the charge is ____ C and the charge is located at x = _____ m.

Explanation / Answer

E = q/(4r2)

we have two unknowns , that are, q and r.

say the charge is 'q' located at 'a' on the x-axis.

For x=2 , E = 5200

=> q/ (x-2)2 = 5200 * 4 ---------- (1)

For x=5 , E =1300

=> q/ (x-5)2 = 1300 * 4 ------------ (2)

dividing (1) / (2),

(x-5)2/(x-2)2 = 4

=> (x-5)/(x-2) = 2

=> x-5 = 2x - 4

x = -1 m

=> q = 5200 * 9 * 4 * 8.854 x 10-12 = 5.21 * 10-6 C = 5.21 C

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