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.

Two small aluminum spheres, each having mass 0.0250 kg, are separated by 80.0 cm. (a) How many electrons does each sphere contain? (The atomic mass of aluminum is 26.982 g/mol, and its atomic number is 13.)

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about 20,000 C/s; this lasts for 100 ms or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

What mass of aluminum has a total nuclear charge of 1.0 C? Aluminum has atomic number 13.

A proton orbits a long charged wire, making 1.0×10^6 revolutions per second. The radius of the orbit is 1.0 cm. What is the wire's linear charge density?

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 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?