Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evalu A- Case 1: Inside the wire Since. r falls inside the wire, then all the enclosed charge must be: Penc On the other hand, the Gaussian surface inside the wire is given by A Using Equation 1, the electric field in simplified form is E=
Q: A Gaussian surface with rectangular size has a positive point charge +q at its center, as shown in…
A: We know that when charge is proportional to the flux i.e., according to Gauss's Law-…
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: The expression for Gauss's law, ∮E→.dA→=qenc/ε0 So, EA=qenc/ε0
Q: A point charge Q is located on the axis of a disk of radius R at a distance h from the plane of the…
A:
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: The Gauss law states that the total flux passing through a closed surface is equal to the charge…
Q: ric charge Q is distributed uniformly along a thick and enormously long conducting wire v dicular to…
A: Suppose an electric field charge (Q) is distributed uniformly along a thick and enormously long…
Q: The figure below shows a very long, thick rod with radius R, uniformly charged throughout. R Find an…
A: Given data, R = radius of the cylindrical rod λ=linear charge density on the rod
Q: Two very long lines of charge are parallel to each other. One with a linear charge density −λ−λ ,…
A:
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: According to the Gauss's law " the total electric flux passes through the closed gaussian surface (…
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: Gauss law is defined as ∮E→·dA→ =qencε0 Here E→ is the electric field, dA→ is a differential area…
Q: Consider a cube with edge length Limmersed in a uniform electric field E along the x-direction as…
A:
Q: The figure below represents the top view of a cubic gaussian surface in a uniform electric field E…
A: It is given a top view of the cubic Gaussian surface in a uniform electric field E→ oriented…
Q: The figure above shows a closed Gaussian surface in the shape of a cube of edge length d. It lies in…
A: The differential form of Gauss law can be given as, Here ρenc is the charge density and E is the…
Q: Consider this sphere. How can we prove that the size of the closed surface is independent of the net…
A: Solution: The surface is not flat and the electric field is not uniform, so to calculate the…
Q: An infinite thin, straight wire has a positive charge distribution (lambda), use a finite cylinder…
A:
Q: Find the electric field of an infinite, flat sheet with charge distribution σ = 17.7 × 10^−12C/m2 by…
A: Given data: Charge density σ=17.7×10-12 C/m2 Radius r = 15 m Distance between new sheet and infinite…
Q: A circular plane, with radius of 2.2 m, is immersed in an electric field with a magnitude of 800…
A: As per guidelines, question 1 is answered. For the remaining questions to be answered post them…
Q: What is the electric flux through a sphere of radius 4 m that contains a (a) +50 uC and (b) -50 uC…
A: a) The given charge inside the sphere is +50 µC. The required electric flux through the given sphere…
Q: A semicircle of radius a is in the first and second quadrants, with the center of curvature at the…
A:
Q: A Gaussian surface with rectangular size has a positive point charge +q at its center, as shown in…
A: According to Gauss law, the total electric flux through any surface that completely surrounds the…
Q: Consider the electric dipole shown in the figure below, formed by two charges, one of which is…
A: Given, the electric dipole shown in the figure below, formed by two charges, one of which is…
Q: An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with…
A:
Q: An infinite, uniform, line of charge is on the x-axis. The linear charge density is (lambda), with…
A: As per our guidelines, only first three sub-parts of a multi-part question are answered. If specific…
Q: Consider a planar disc of radius 12cm that makes some angle 30∘ with the uniform electric field of…
A: Radius of planer disk: r = 12 cm = 0.12 m Magnitude of uniform magnetic field: E = 500 N/C Angle…
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: Total charge is Q . Area is A = 2πrL Where r is the radius L is the Length of the cylindrical…
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: Given data: Magnitude of total charge is, Q.
Q: For an infinitely long wire with uniform line-charge density, 2, along the z-axis, the electric…
A:
Q: Consider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and a…
A: lets us first solve the question for general arc with assumed angle in the figures below:
Q: Use Gauss's law (OE•dà ) to show that the electric field a distance r away from the axis enc of an…
A:
Q: A sphere of Radius rɔ carries a constant volume charge density po as seen in the figure. A spherical…
A: Given data: The radius of the sphere is r0. The volume charge density of the sphere is ρ0. The…
Q: Use GFSA (Given, Find, Solution, and Answer) on the given space below. Encircle your final answer,…
A: Given data: Radius of the cylinder, r = 1m length of the cylinder, l =1.5 m Linear charge…
Q: We have chosen a potato-like Gaussian surface to evaluate Y12Q8 the electric flux emitted from an…
A: Given a potato-shaped Gaussian surface. Charges are inside the volume 'V' bounded by the surface S.…
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: Recall Gauss's law ∮E→.dA→=qenc/∈0
Q: A point charge Q is located on the axis of a disk of radius R at a distance h from the plane of the…
A:
Q: Consider a solid spherical conductor of radius R and charge Q at electrostatic equilibrium shown…
A:
Q: In each of the four cases belowa Gaussian circle is represented by the dashed line circle and the…
A:
Q: A charge q is placed in the cavity of a conductor as shown below. Will a charge outside the…
A: Ans:- Image-1
Q: Compute for the work done, in millijoules, in moving a 6-nC charge radially away from the center…
A: Since you have posted a question with multiple sub-parts, as per our guidelines we will solve first…
Q: A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a…
A:
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A:
Q: Not considering the enclosed charge, or just considering the flux, explain what factor could…
A: Flux is total number of electric field lines crossing the surface.
Q: Find the electric field everywhere of an infinite uniform line charge with total charge Q. Sol.…
A: Suppose charge enclosed in the gaussian surface is qenc and radius of cylinder is 'r', then Using…
Q: Another special case turns out to be of considerable interest. Let's see what the electric field is…
A:
Q: An infinite, uniform, line of charge is on the x-axis. The linear charge density is (lambda), with…
A: (c) The total charge enclosed by the surface is, The net flux enclosed on the uniform line of…
Q: Discuss the possibility of choosing Gaussian surface other than the sphere. For instance what if you…
A:
Q: The charge per unit length on the thin rod shown below is 2. What is the electric field at the point…
A:
Q: perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the…
A: Suppose an electric field charge (Q) is distributed uniformly along a thick and enormously long…
Q: Consider a set oftwo stationary point charges q, and q, as shown in the figure. Which of the…
A: In Gaussian surface electric field is considered of all charges whether it is present or not inside…
Step by step
Solved in 2 steps
- Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed uniformly throughout its volume. (a) is the electric force exerted on an electron when it is 3.01015 m from the center of the nucleus? (b) What is the acceleration of the electron at this point?A long cylinder of aluminum of radius R meters is charged so that it has a uniform charge per unit length on its surface of . (a) Find the electric field inside and outside the cylinder. (b) Plot electric field as a function of distance from the center of the rod.A total charge Q is distributed uniformly throughout a spherical volume that is centered at o1 and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at o2 (see below). Show that the electric field everywhere in the empty region is given by E=Qr40R3 where r is the displacement vector directed from o1 to o2 .
- Shown below ale two concentric conducting spherical shells of radii R1 and R2 , each of finite thickness much less than either radius. The inner and outer shell carry net charges q1 and q2 , respectively, where both q1 and q2 are positive. What is the electric field for (a) rR1 ; (b) R1rR2 , and (c) rR2 ? (d) What is the net charge on the inner surface of the inner shell, the outer surface of the inner shell, the inner surface of the outer shell, and the outer surface of the outer shell?The infinite slab between the planes defined by z=a/2 and z=a/2 contains a uniform volume charge density p (see below). What is the electric field produced by this charge distribution, both inside and outside the distribution?A solid cylindrical conductor of radius a is surrounded by a concentric cylindrical shell of inner radius b. The solid cylinder and the shell carry charges +Q and Q , respectively. Assuming that the length L of both conductors is much greater than a or b, determine the electric field as a function of r, the distance from the common central axis of the cylinders, for (a) ra; (b) arb; and (c) rb.
- Problem An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distancer perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside atr distance from the wire we will use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc = On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E = Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc = On the other hand, the Gaussian surface outside the wire is given by A = Using Equation 1, the electric field in…Problem An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as qenc / epsilono We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A= genc epsilond (Equation 1) E Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: denc = On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E = Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc = On the other hand, the Gaussian surface outside the wire is given by A = Using…An infinitely long non conducting wire ef înner radius R and outer radius 2R. The volumetric charge density af the cylindrical shell is given by the expressicn r-Kr Here K is a positive constant andr îs the distance from the axis af the cylinder a) Find the electric field în the region > 2R using Gauss's law. b) Find the potential ditterence VB-VA Using electric tield the you found. -p=Kr 2R A -3R -AR-
- Consider a thin plastic rod bent into an arc of radius Rand angle a (see figure below). The rod carries a uniformly distributed negative charge Q -Q A IR What are the components and E, of the electric field at the origin? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the AE contributed by a representative piece. (b) Express algebraically the contribution each piece makes to the and y components of the electric field. Be sure to show your integration variable and its origin on your drawing. (Use the following as necessary: Q, R, cx, 0, A0, and EQ-) ΔΕ, = - TE aR² AB=(2 Lower limit= 0 ✓ e aR² Upper limit= a X cos(0)40 x (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. sin (0)40 x Evaluate the integral. (Use the following as necessary: Q, R, a, and E.) EditProblem An electric charge Q is distributed uniformly along a thick and enormously long conducting wire with radius R and length L. Using Gauss's law, what is the electric field at distance r perpendicular to the wire? (Consider the cases inside and outside the wire) Solution To find the electric field inside at r distance from the wire we will use the Gauss's law which is expressed as We will choose a symmetric Gaussian surface, which is the surface a cylinder excluding its ends, then evaluate the dot product to obtain A = (Equation 1) Case 1: Inside the wire Since, r falls inside the wire, then all the enclosed charge must be: qenc = On the other hand, the Gaussian surface inside the wire is given by A = Using Equation 1, the electric field in simplified form is E = Case 2: Outside the wire Since, r falls outside the wire, then, all the charge must be enclosed, thus denc = On the other hand, the Gaussian surface outside the wire is given by A = Using Equation 1, the electric field in…Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius Rand total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q. we recall that the electric field it produces at distance x0 is given by E = (1/ 2-2) Since, the actual ring (whose charge is da) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as 2. = (1/ We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E = (x0/ 2.…