A line of charge starts at x = + x 0 and extends to positive infinity. The linea

Question

A line of charge starts at x = +x0 and extends to positive infinity. The linear charge density is ? = ?0x0/x, where ?0 is a constant. Determine the electric field at the origin. (Use any variable or symbol stated above along with the following as necessary: ke.)

A line of charge starts at x = +x0 and extends to positive infinity. The linear charge density is ? = ?0x0/x, where ?0 is a constant. Determine the electric field at the origin. (Use any variable or symbol stated above along with the following as necessary: ke.) Find vector E

Explanation / Answer

E = integral of k*lambda*dx/x^2 = integral of k*lambda0*x0*dx/x^3 = -k*lambda0*x0/2x^2

integrated from x0 to infinity it gives

E = k*lambda0*x0*(0-1/2x0^2 ) = k*lambda0/2x0

E = - k*lambda0/2x0 i N/C

bold letter represents vector notation and i is the unit vector in x-direction

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