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Linear Charge Density Problems: Electric Field Calculation Example

Solve problems involving linear charge density to calculate electric field at a given point. Example with step-by-step calculation and exercise for students.

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Linear Charge Density Problems: Electric Field Calculation Example

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  1. PROBLEM SOLVING EXAMPLE Maria Dworzecka

  2. Linear charge density – Examples y P r dq=ldx h x We know: x a What is ? (A) (B) (C) (D) (E) Charge is uniformly distributed along the x-axis from the origin to x = a. The charge density is l[C/m] . What is the x-componentof the electric field at point P: (x,y) = (a,h)?

  3. Calculation P y r h q1 q2 x x a dq=ldx What is ? (A) (B) (C) (D) q2 We know:

  4. Calculation P y r h q1 q2 x x a dq=ldx What is? (A) (B) (C) none of the above q2 Weknow: cosq2 DEPENDS ON x !! 3

  5. Calculation P y r h q1 q2 x x a dq=ldx What is ? (D) (B) (C) (A) q2 We know:

  6. Calculation P y r h q1 q2 x x a dq=ldx What is ? q2 Weknow:

  7. Observation P y r h Note that our result can be rewritten more simply in terms of q1. q1 q2 x x a dq=ldx q2 Exercise for student: Change variables: write x in terms of q Result: obtain simple integral in q 33

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