Let the vector field

A sphere of radius is at the center of an orthogonal coordinate system. Inside the sphere, we place an orange shape with volume charge density . We need to find the electric field on the surface of the outer sphere. Which of the following questions are(is) correct?

A parallel-plate capacitor has plate area A=0.02 m2A = 0.02 \, \text{m}^2 and separation d=1 mmd = 1 \, \text{mm}.It is connected to a constant voltage source of V = [x] V. If the upper plate is allowed to move slightly while the voltage is maintained constant, what is the magnitude (in μN, one decimal place) of the attractive force acting on the upper plate due to the electric field? (the material between the plates is air).

What is the fundamental difference between an insulator, a semiconductor, and a conductor?

Ampère’s circuital law in integral form is given by: Which of the following best describes the meaning of this equation?  

If the line integral of the magnetic field intensity H\mathbf{H} over a closed contour is zero, does it necessarily follow that H=0\mathbf{H} = 0 at every point on the contour?

A proton enters a region with magnetic field B⃗=B0z^ and velocity v⃗=v0(x^+z^). What is the magnitude of the magnetic force on the proton?

Two infinitely long parallel wires carry currents of equal magnitude. What is the resultant magnetic field due to the two wires at a point midway between the wires—compared with the magnetic field due to one of them alone—if the currents are in opposite directions? (Choose all the correct answers).

An electron (, ) enters a uniform magnetic field B= [x] with speed

Two infinitely long parallel wires carry currents of equal magnitude. What is the resultant magnetic field due to the two wires at a point midway between the wires—compared with the magnetic field due to one of them alone—if the currents are in the same direction? (Choose all the correct answers).