---### Problem Statement: Electric Field CalculationConsider a thin, spherical shell of radius \( 14.5 \) cm with a total charge of \( 29.9 \) μC distributed uniformly on its surface.#### (a) Find the electric field 10.0 cm from the center of the charge distribution.#### (b) Find the electric field 24.5 cm from the center of the charge distribution.---### ExplanationTo solve these problems, we will apply Gauss's Law, which relates the electric field to the charge enclosed by a Gaussian surface. The electric field \( E \) due to a spherical charge distribution can be calculated differently depending on whether the point of interest is inside or outside the spherical shell:1. **Inside the Spherical Shell ( \( r < R \) )**: - For any point inside a uniformly charged spherical shell, the electric field is zero because the charges on the shell produce a net zero electric field inside.2. **Outside the Spherical Shell ( \( r \geq R \) )**: - The electric field due to a spherical shell of charge is as if all the charge were concentrated at the center of the shell. Thus, it can be calculated using Coulomb's Law: \[ E = \frac{1}{4\pi \epsilon_0} \frac{Q}{r^2} \] where \( \epsilon_0 \) is the permittivity of free space, \( Q \) is the total charge, and \( r \) is the distance from the center of the sphere.Let's solve the problems step-by-step.### Solution#### (a) Electric Field at 10.0 cm from the CenterSince \( 10.0 \) cm is less than the radius \( 14.5 \) cm (i.e., \( r < R \)), according to Gauss's Law, the electric field inside a spherical shell is zero.\[E_{\text{inside}} = 0\]Thus, the electric field 10.0 cm from the center of the charge distribution is:\[\boxed{0}\]#### (b) Electric Field at 24.5 cm from the CenterSince \( 24.5 \) cm is greater than the radius \( 14.5 \) cm (i.e., \( r \geq R \)), we

a. According to the Gauss’s law, the electric flux is

Consider a thin, spherical shell of radius 14.5 cm with a total charge of 29.9 µC distributed uniformly on its surface. (a) Find the electric field 10.0 cm from the center of the charge distribution. (b) Find the electric field 24.5 cm from the center of the charge distribution.

Consider a thin, spherical shell of radius 14.5 cm with a total charge of 29.9 µC distributed uniformly on its surface. (a) Find the electric field 10.0 cm from the center of the charge distribution. (b) Find the electric field 24.5 cm from the center of the charge distribution.

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

A nonconducting solid sphere of radius 10.7 cm has a uniform volume charge density. The magnitude of the electric field at 21.4 cm from the sphere's center is 2.18 103 N/C. (a) What is the sphere's volume charge density? (b) Find the magnitude of the electric field at a distance of 5.00 cm from the sphere's center.
A solid sphere of radius 40.0 cm has a total positive charge of 25.0 µC uniformly distributed throughout its volume. Calculate the magnitude of the electric field at the following distances. (a) 0 cm from the center of the sphere kN/C(b) 10.0 cm from the center of the sphere kN/C(c) 40.0 cm from the center of the sphere kN/C
A charge of 22.2 pC is distributed uniformly on a spherical surface (r = 2.0 cm), and a second charge of – 14.1 pC is distributed uniformly on a concentric thin spherical surface (r2 = %3D 4.0 cm). Determine the magnitude of the electric field ( in units of N/C) at a distance of 5.0 cm from the center of the two surfaces.
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 sphere with a radius of 0.220 m has a uniform charge density and a total charge of 71.3 mC. What is the magnitude of the electric field at each of the following locations? (a) a distance of 0.130 m from the center N/C(b) a distance of 0.220 m from the center N/C(c) a distance of 0.800 m from the center N/C
Consider a thin, spherical shell of radius 13.0 cm with a total charge of 35.2 µC distributed uniformly on its surface.
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 square conducting plate 54.0 cm on a side and with no net charge is placed in a region, where there is a uniform electric field of 75.0 kN/C directed to the right and perpendicular to the plate. (a)Find the charge density (in nC/m2) on the surface of the right face of the plate. b)Find the charge density (in nC/m2) on the surface of the left face of the plate. (c)Find the magnitude (in nC) of the charge on either face of the plate.
An unknown charge sits on a conducting solid sphere of radius 9.5 cm. If the electric field 13 cm from the center of the sphere has magnitude 4.3 × 103 N/C and is directed radially inward, what is the net charge on the sphere?
Solve it correctly.
A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C find(a) The net charge on the shell and(b) The electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.
An arc of charge is in the first quadrant. It has a charge of 0.098nG uniformly distributed along its length. The radius of the arc is 17.1cm. Determine the magnitude of the electric field vector at the point (0,0) in