### Problem StatementA uniformly charged disk with radius \( R = 40.0 \) cm and uniform charge density \( \sigma = 8.90 \times 10^{-3} \) C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations?#### (a) \( z = 5.00 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]#### (b) \( z = 10.0 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]#### (c) \( z = 50.0 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]#### (d) \( z = 200 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]### Explanation for Educational WebsiteThis problem involves calculating the electric field generated by a uniformly charged disk at different points along the z-axis.#### Definitions:- **Radius (R):** The distance from the center of the disk to its edge.- **Uniform charge density (\(\sigma\)):** Charge per unit area on the surface of the disk.- **xy-plane:** A two-dimensional plane determined by the x-axis and y-axis.#### Strategy:Use the formula for the electric field due to a uniformly charged disk at a point along its perpendicular axis (the z-axis):\[ E(z) = \frac{\sigma}{2 \epsilon_0} \left( 1 - \frac{z}{\sqrt{z^2 + R^2}} \right) \]where:- \( z \) is the distance from the disk along the z-axis.- \( \epsilon_0 \) is the permittivity of free space (\( \epsilon_0 \approx 8.85 \times 10^{-12} \text{C}^2/(\text{N} \cdot \text{m}^2) \)).#### Steps:1. **Convert cm to m:** Ensure all distances are in meters for consistency in units.2. **Substitute values into the formula:** Plug in the radius \( R \), charge density \( \sigma \), and distance \( z \)

Hi, as this problem contains multiple sub-parts, hence the first three sub-parts will be solved for…

A uniformly charged disk with radius R = 40.0 cm and uniform charge density = 8.90 x 10-3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm MN/C (b) z 10.0 cm MN/C (c) z = 50.0 cm MN/C (d) z = 200 cm MN/C

A uniformly charged disk with radius R = 40.0 cm and uniform charge density = 8.90 x 10-3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm MN/C (b) z 10.0 cm MN/C (c) z = 50.0 cm MN/C (d) z = 200 cm MN/C

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

162. In Fig. 68, the ring of radius R=30 cm, mass m=4 g and uniform linear charge density of X=4.10-³ C/m, is in equilibrium in a horizontal plane, in the presence of the spherical charge that is at a distance d=40 cm from the center of the ring. Find the value of the electric charge of the sphemite. (k = 9.10° N.m²/C2, u = 10°) a) 18,0 UC b)18,2 UC c)18,4 uc d) 18,6 uc Fig.68 e)18,8 UC
2.1
+X, to positive infinity. The line carries positive charge with a uniform linear charge density Ao. A continuous line of charge lies along the x axis, extending from x = (a) What is the magnitude of the electric field at the origin? (Use the following as necessary: 1o, xo, and ke.) 0. %3D (b) What is the direction of the electric field at the origin? O +X +y O -z
A point charge q = -5.5x 10 C is placed at the center of a spherical conducting shell of inner radius 2.8 cm and outer radius 3.3 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 9.0 N/C. (a) What is the charge density (in C/m2) on the inner surface of the shell? C/m² (b) What is the charge density (in C/m2) on the outer surface of the shell? C/m² (c) What is the net charge (in C) on the conductor?
A solid conducting sphere of radius 2.00 cm has a charge 17.00 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge of -6.00 µC. (Take radially outward as the positive direction.) (a) Find the electric field at r = 1.00 cm from the center of this charge configuration. MN/C (b) Find the electric field at r = 3.00 cm from the center of this charge configuration. MN/C (c) Find the electric field at r = 4.50 cm from the center of this charge configuration. MN/C (d) Find the electric field atr = 7.00 cm from the center of this charge configuration. MN/C
A uniformly charged disk with radius R = 40.0 cm and uniform charge density = 8.90 x 10-3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (In MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm (b) z 10.0 cm (c) z = 50.0 cm™ (d) z 200 cm MN/C MN/C MN/C MN/C
A charge of –25 µC is distributed uniformly over the surface of a spherical conductor of radius 11.0 cm. Determine the electric field (in N/C) due to this charge at the following distances from the center of the sphere. (Enter the radial component of the electric field.) (a) 7.0 cm E - (0 = (b) 8.0 cm E = (c) 22.0 cm E = X N/C f
A uniformly charged disk with radius R = 45.0 cm and uniform charge density & = 6.70 x 10-³ C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z 5.00 cm (b) z = 10.0 cm (c) z = 50.0 cm (d) z = 200 cm MN/C MN/C MN/C MN/C
A horizontal charged disk has a radius of 0.06 m and a uniform surface charge density of p, = 2.34 x 10 C/m². It is centered on the z axis and is located 0.2 m below the xy plane. A point charge of Q = 1 μC is located at the origin. Calculate the force acting on the disk as a result of the electric field intensity produced by the point charge.
Two conducting hollow spheres share a common center. The inner sphere has the radius a = 5.0 cm and charge +3.2x10-6 C. The outer sphere has the radius b = 32 cm and charge -4.0x10-6 C. What is the electric field (in N/C) at a point P, r = 20 cm from the center of the spheres?
Solve it correctly.
+ a + A hollow sphere has a uniform volume charge density of 1.46 nC/m3. The inner radius is a = 11.7 cm and the outer radius is b = 46.8 cm. What is the magnitude of the electric field at 4.68 cm from the center of the sphere? What is the magnitude of the electric field at 145 cm from the center of the sphere?