Electric field of a point charge
Section: Electric Fields | Syllabus: Cambridge AS Level Physics 9702
Field Strength Formula The electric field E at a distance r from a point charge Q is determined by substituting Coulomb's law into the definition E = F/q. E = Q/4πε_0 r^2 The field is radial and follows the inverse square law.
For multiple charges, the resultant field is the vector sum of individual fields. Worked Examples Worked Example: Resultant Field between Spheres Question: Two spheres (+Q and -Q) are 10.0 cm apart. The resultant field at point X (3.0 cm from +Q) is 6.0 × 10^4 N C^-1.
Determine Q. Solution 1. Both fields point to the right (away from +Q, towards -Q). 2. E_total = E_+ + E_- = Q/4πε_0 r_1^2 + Q/4πε_0 r_2^2. 3. 6.0 × 10^4 = Q/4πε_0 ( 1/0.03^2 + 1/0.07^2 ). 4. 6.0 × 10^4 = Q × (8.99 × 10^9) × (1111.1 + 204.1).
5. Q = 6.0 × 10^4/1.18 × 10^13 = 5.1 × 10^-9 C. Worked Example: Perpendicular Fields Question: Point P is 40 mm from two +5.0 nC charges in perpendicular directions. Determine the strength of the resultant field.
Solution 1. E_1 = E_2 = kQ/r^2 = 8.99 × 10^9 × 5.0 × 10^-90.04^2 = 2.81 × 10^4 N C^-1. 2. Resultant field E = √E_1^2 + E_2^2 = E_1 √2. 3. E = 2.81 × 10^4 × 1.41 = 3.97 × 10^4 N C^-1.
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