Problem 7: Show that the equation below, for the electric field of a charged disk at...
The total electric field at a point on the axis of a uniformly charged disk, which has a radius R and a uniform charge density of σ, is given by the following expression, where x is the distance of the point from the disk. (R2 + x2)1/2 Consider a disk of radius R-3.18 cm having a uniformly distributed charge of +4.83 C. (a) Using the expression above, compute the electric field at a point on the axis and 3.12 mm...
The total electric field at a point on the axis of a uniformly charged disk, which has a radius R and a uniform charge density of σ, is given by the following expression, where x is the distance of the point from the disk. (R2 + x2)1/2 Consider a disk of radius R-3.27 cm having a uniformly distributed charge of +5.18 C. (a) Using the expression above, compute the electric field at a point on the axis and 3.30 mm...
P (a) (b) +29 ( c) + -Q (d) FIGURE 21-34 Electric field lines for four arrangements of charges. E P R do EXAMPLE 21-12 Uniformly charged disk. Charge is distributed uniformly over a thin circular disk of radius R. The charge per unit area (C/m²) is o. Calculate the electric field at a point P on the axis of the disk, a distance z above its center, Fig. 21-30. APPROACH We can think of the disk as a set...
Show steps of derivation from equation (22-26) to (22-27) please include explanations. Thank you. where we have pulled the constants (including z) out of the integral. T this integral, wecast it in the form f X ndX by setting X = (z2 + r2). )o solve and dx (2r) dr. For the recast integral we have m+ 1 and so Eq. 22-24 becomes (22-25) 0 Taking the limits in Eq. 22-25 and rearranging, we find (22-26) 2e(charged disk) as the...
Answer is Below. Problem 3: Consider a disk of radius R in the xy-plane with a non-uniform surface charge density ơ(r)-ar, where a > 0 is a constant. Determine the electric field at a point z above the disk, along its axis of symmetry
The electric field along the axis of a uniformly charged disk of radius R and total charge Q is given below. Ex = 2πkeσ 1 − x (x2 + R2)1/2 Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q = σπR2. Suggestion: First show that x (x2 + R2)1/2 = 1 + R2 x2 −1/2 , and use the binomial expansion (1 + δ)n ≈ 1 +...
Using the form for the electric field of a uniformly charged disk of radius R, determine the far field limit of the electric field at a point on the central axis.
Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 4.60R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/4.60 (see Figure (b)). Assume that the ring will have the same surface charge...
A charged disk and a charged ring are centered at the origin in the free space as shown in figure 4. Bothe changed elements exists in the xy plane. The disk has a radius a and carries a uniform surface charge density of Ps. The ring has a radius 2a and carries a uniform line charge density Pe. Find the following: a) The electric field intensity on z-axis and determine where the electric field is zero b) The electric potential...