I need help figuring out this practice problem. Please provide a complete detail

Question

I need help figuring out this practice problem. Please provide a complete detailed explanation. Thanks.
Four point charges with charges +4 µC, +4 µC, -4 µC, and -4 µC in this order, are placed at the four corners of a square that is 20 cm on a side. Find the electric field at the center of the square? ans: 5.1e6 N/C
I need help figuring out this practice problem. Please provide a complete detailed explanation. Thanks.
Four point charges with charges +4 µC, +4 µC, -4 µC, and -4 µC in this order, are placed at the four corners of a square that is 20 cm on a side. Find the electric field at the center of the square? ans: 5.1e6 N/C

Explanation / Answer

field at center due to +4 uC is E = Kq / r ^ 2 where K = coulomb's constant = 8.99 * 10 ^ 9 Nm^ 2/C^ 2 q = charge = 4 * 10^-6 C r = distanc eof hte center from corner = a / sqrt(2) a = side = 20 cm =0.2 m r = 0.1414 m plug th values we get E = 1.798* 10^6 N / C field at center due to -4 uC is E ' = Kq ' / r ^ 2 where K = coulomb's constant = 8.99 * 10 ^ 9 Nm^ 2/C^ 2 q' = charge = -4 * 10^-6 C r = distanc eof hte center from corner = a / sqrt(2) a = side = 20 cm =0.2 m r = 0.1414 m plug th values we get E ' = 1.798* 10^6 N / C both E and E ' are in same direction. So, net electric field E " = E + E ' = 3.596* 10^6 N / C field at center due to another +4 uC is e = Kq / r ^ 2 where K = coulomb's constant = 8.99 * 10 ^ 9 Nm^ 2/C^ 2 q = charge = 4 * 10^-6 C r = distanc eof hte center from corner = a / sqrt(2) a = side = 20 cm =0.2 m r = 0.1414 m plug th values we get e = 1.798* 10^6 N / C field at center due to -4 uC is e ' = Kq ' / r ^ 2 where K = coulomb's constant = 8.99 * 10 ^ 9 Nm^ 2/C^ 2 q' = charge = -4 * 10^-6 C r = distanc eof hte center from corner = a / sqrt(2) a = side = 20 cm =0.2 m r = 0.1414 m plug th values we get e ' = 1.798* 10^6 N / C both E and E ' are in same direction. So, net electric field e " = e + e ' = 3.596* 10^6 N / C both E " and e " are perpendicular to each other. So, net electric field E"' = sqrt [ E"^ 2+ e"^ 2] = 5.08 * 10^6 N / C

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.