The electric potential at point P due to the point charges and q2 is the algebra

Question

The electric potential at point P due to the point charges and q2 is the algebraic sum of the potentials due to the individual charges. Suppose a charge of -1.70 muC is at the origin and a charge of 3.10 muC is at the point (0, 3.00) m. Find the electric potential at (4.00, 0) m, assuming the electric potential is zero at infinity. Find the work necessary to bring a 4.10 muC charge from infinity to the point (4.00, 0) m.

Explanation / Answer

sqrt(4²+3²) = 5 m ---> vector length from charge 2 to desired point theta = tan^-1(3/4) = 36.87º ---> angle above x axis for that vector the electric field is a vector quantity, so E1 + E2 = E E = F / q , where F = k q1 q2 / r² for E1 (all in the j direction) E1 = k q1 q2 / (q2 r²) = kq1 / r² j = (8.99E9)(-1.7E-6)/(3²) = 1698.11 N/C j for E2 (i and j directions) E2 = k q1 q2 / (q1 r²) = kq2 / r² (cos ? i + sin ? j) = [(8.99E9)(3.1E-6) / (5²)] (cos 36.87º i + sin 36.87º j) = 891.80 N/C i + 667.77 N/C j Now add E1 + E2 E = 1698.11 i + 891.80 N/C i + 667.77 N/C j = 2589.91 N/C i + 667.77 N/C j E = sqrt(2589² + 667.77² ) E = 2674.61 N/C

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