A thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x)=λ₀x/L, where x is measured from the rod's left end.a. What is λ₀ in terms of Q and L?

CALC A 12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nC/cm)e−|x|/(6.0 cm) , where x is measured from the center of the rod. What is the total charge on the rod?Hint: This exercise requires an integration. Think about how to handle the absolute value sign.

CALC A rod of length L lies along the y-axis with its center at the origin. The rod has a nonuniform linear charge density λ=a|y|, where a is a constant with the units C/m^2.b. Determine the constant a in terms of L and the rod's total charge Q.

A 20-cm-radius ball is uniformly charged to 80 nC. (b) How much charge is enclosed by spheres of radii 5, 10, and 20 cm?

An infinite cylinder of radius R has a linear charge density λ . The volume charge density (C/m³) within the cylinder (r ≤ R ) is p (r) = rp₀ / R, where p₀ is a constant to be determined. (b) The charge within a small volume dV is dq = p dV. The integral of p dV over a cylinder of length L is the total charge Q = λ L within the cylinder. Use this fact to show that p₀ = 3λ / 2πR² Hint: Let dV be a cylindrical shell of length L, radius r, and thickness dr. What is the volume of such a shell?

A glass rod is rubbed with silk, and a plastic rod is rubbed with wool. Afterward, to which object or objects will the glass rod be attracted?

A ring of charge lies in the xy-plane with its center at the origin. The ring has a radius of 87 cm and a total charge of $130\mu \mathrm{C}$. What is the linear charge density on the ring?