Question

A cylindrical shell with radius R and length W carries a uniform chargeQ and rotates about its axis with angular speed ω. The center of the cylinder lies at the origin O and its axis is coincident with the x-axis, as shown in (Figure 1).

Part A

What is the charge density σ?

Express your answer in terms of the variables Q, R, and W.

σ =______________

Part B

What is the differential current dI on a circular strip of the cylinder centered at x and with width dx?

Express your answer in terms of the variables σ, R, ω, anddx.

dI=______________

Part C

Use Bx = $\frac{\mu _0Ia^2}{2(x^2 + a^2)^\frac{3}{2}}$ to write an expression for the differential magnetic field dB⃗  at the origin due to this strip.

Express your answer in terms of the variables Q, R,ω, W,x, μ₀, and dx.

dB₀(x)______________

Part D

Integrate to determine the magnetic field at the origin.

Express your answer in terms of the variables Q, R,ω, W, and$\mu _0$.

B⃗ (0) = ______________

Answer 1