1. Find the expressions of the static Coulomb's field E = Q ŕ Απεργ2 in the Cartesian and cylindrical coordinates. Hint: you need to determine the inner products among the unit vectors in different coordinate frames.

The figure below shows four small charged spheres arranged at the corners of a square with side d = 25.0 cm. (Let q₁ = +4.00 nC, 92 = +6.00 nC, 93 = +9.00 nC, and 94 = +5.00 nC. Assume 93 is located at the origin and +x axis is to the right and the +y axis is up along the page. Express your answers in vector form.) 91 d 92 93 d 94 (a) What is the electric field at the location of the sphere with charge +9.00 nC? N/C (b) What is the total electric force exerted on the sphere with charge +9.00 nC by the other three spheres? = N d d

L vo y E A uniform field E = -150000j N/C exists between two plates of length L = 3 cm, as shown in the figure above. A proton is fired at an angle of 40° to the x axis with an initial speed of 7300000 m/s. a) Find its vertical coordinates as it emerges from the plate, assuming the proton will not hit any plate in the process. cm b) Find the angle at which it emerges. degrees to the x axis.

An electron travels from right to left at 3 x 10° m/s when it encounters the B field pictured below. The magnitude of the field is 1Tesla. Draw a picture of the electron's path in the field with the correct direction. Calculate the radius of curvature. х х

— Your answer is partially correct. Multiple-Concept Example 3 provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 2.92 × 10-¹1 m. Determine the magnitude of the electron's centripetal acceleration. Number i 5.9E23 Units m/s^2

A single proton is accelerated in a uniform E-field (directed eastward) at 3.2x10^8 m/s^2. Find the magnitude of the field and direction of the acceleration.

Answer: A. Which ball (one on the right or one on the left) has a positive charge? B. What is the Magnitude E of the field?

Give an example of a nonconstant field with zero divergence.  Give an example of a field with a constant negative divergence.

Round to three significant figures.

What is the magnitude of the total field at the point x = 0, z = 1.00 m in the xz-plane? What is the magnitude of the total field at the point x = 1.00 m, z = 0 in the xz-plane? What is the magnitude of the total field at the point x = 0, z = -0.25 m in the xz-plane?