A rod of length L lies along the x-axis with its left end at the origin. The rod has a non-uniformcharge density λ = ax, where a is a positive constant.P(a) Express the total charge Q on the rod in terms of a and L.(b) Calculate the electric field at point P, shown in the Figure. Take the limit d » L. What doesthe electric field look like in this limit? Is this what you expect? Explain. Hint: the followingintegral may be useful:x dx(x+a)²In(1+x)=x-a -+ln(x + a)Xx + a+²2+... (for small .x)

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A rod of length L lies along the x-axis with its left end at the origin. The rod has a non-uniform charge density λ = ax, where a is a positive constant. (a) Express the total charge on the rod in terms of a and Z. (b) Calculate the electric field at point P, shown in the Figure. Take the limitd > L. What does the electric field look like in this limit? Is this what you expect? Explain. Hint: the following integral may be useful: a x dx = +In(x+a) (x+a)² x+a x² In(1+x)=x-+ x 2 (for small .x)

A rod of length L lies along the x-axis with its left end at the origin. The rod has a non-uniform charge density λ = ax, where a is a positive constant. (a) Express the total charge on the rod in terms of a and Z. (b) Calculate the electric field at point P, shown in the Figure. Take the limitd > L. What does the electric field look like in this limit? Is this what you expect? Explain. Hint: the following integral may be useful: a x dx = +In(x+a) (x+a)² x+a x² In(1+x)=x-+ x 2 (for small .x)