Electric Fields with Calculus Video Lessons

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Problem: A total charge Q is distributed uniformly over rod length L. The rod is aligned on the x-axis, with one end at the origin and the other at point x = L.a) calculate electric field at a point (0,D) b) calculate the electric field at point (L/2,D)

FREE Expert Solution

This problem required us to calculate the electric field at points (0, D) and at (L/2, D).

Electric field is expressed as:

E=kqr2, where is Coulomb's constant, q is the charge, and r is the distance from the point to the charge. 

q=λL, where λ is the line charge density and is the length. 

a)

Taking an element of the charge, dq:

dq=λdx

We now have, dE = dEcosθ(-i) + dE sinθ (j) ........................(1)

Also,

dE=kdqr2=kλdx(D2+x2)

Substituting this to equation (1):

dE=kλdx(D2+x2)[cosθ(-i)+sinθ(j)]

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Problem Details

A total charge Q is distributed uniformly over rod length L. The rod is aligned on the x-axis, with one end at the origin and the other at point x = L.

a) calculate electric field at a point (0,D) 

b) calculate the electric field at point (L/2,D)

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