Question

In: Physics

An infinite straight wire has a linear charge density of 10 nC/m. What is the electric...

An infinite straight wire has a linear charge density of 10 nC/m. What is the electric

field 0.50 meters away?

Expert Solution

Electric Field of a Uniformly Charged Wire

Consider a long straight wire which carries the uniform charge per unit length . We expect the electric field generated by such a charge distribution to possess cylindrical symmetry. We also expect the field to point radially (in a cylindrical sense) away from the wire (assuming that the wire is positively charged).

**Figure 11:** *The electric field generated by a uniformly charged wire.*

Let us draw a cylindrical gaussian surface, co-axial with the wire, of radius and length --see Fig. 11. The above symmetry arguments imply that the electric field generated by the wire is everywhere perpendicular to the curved surface of the cylinder. Thus, according to Gauss' law,

(70)

where is the electric field-strength a perpendicular distance from the wire. Here, the left-hand side represents the electric flux through the gaussian surface. Note that there is no contribution from the two flat ends of the cylinder, since the field is parallel to the surface there. The right-hand side represents the total charge enclosed by the cylinder, divided by . It follows that

(71)

The field points radially (in a cylindrical sense) away from the wire if , and radially towards the wire if .

E = 10*10^-9/2*3.14*8.85*10^-12*.5

E = 359.854

genius_generous answered 2 months ago

A straight, nonconducting plastic wire 9.00 cm long carries a charge density of 125 nC/m distributed...

A straight, nonconducting plastic wire 9.00 cm long carries a charge density of 125 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. A) Find the magnitude and direction of the electric field this wire produces at a point 6.00 cm directly above its midpoint. B) If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 6.00 cm...

A uniform line charge of linear charge density = 2.9 nC/m extends from x = 0...

A uniform line charge of linear charge density = 2.9 nC/m extends from x = 0 to x = 5 m. a) What is the total charge? b) Find the electric field on the x axis at x = 6 m. c)Find the electric field on the x axis at x = 11 m. d)Find the electric field on the x axis at x = 250 m e) Find the field at x = 250 m, using the approximation that...

An infinite line of charge with linear density λ1 = 7.2 μC/m is positioned along the...

An infinite line of charge with linear density λ1 = 7.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.2 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -562 μC/m3. 1) a) What is λ2, the linear charge density of the insulating shell?____μC/m b) What is Ex(P), the value of the x-component of the electric field at point P,...

A charge (uniform linear density = 6.1 nC/m) lies on a string that is stretched along...

A charge (uniform linear density = 6.1 nC/m) lies on a string that is stretched along an x axis from x = 0 to x = 2.3 m. Determine the magnitude of the electric field at x = 6.5 m on the x axis.

An infinitely long line of charge has a linear charge density of 5.50×10−12 C/m . A...

An infinitely long line of charge has a linear charge density of 5.50×10−12 C/m . A proton is at distance 15.0 cm from the line and is moving directly toward the line with speed 1100 m/s . How close does the proton get to the line of charge? Express your answer in meters.

A charge (uniform linear density = 15 nC/m) is distributed along the x axis from x...

A charge (uniform linear density = 15 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. determine the magnitude of the electric field at a point on the x axis with x = 4.0 m

A charge of uniform linear density 2.20 nC/m is distributed along a long, thin, nonconducting rod....

A charge of uniform linear density 2.20 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 4.00 cm, outer radius = 9.00 cm). The net charge on the shell is zero. (a) What is the magnitude of the electric field at distance r = 13.0 cm from the axis of the shell? What is the surface charge density on the (b) inner and (c) outer surface of...

An infinitely long line of charge has linear charge density 5.00×10−12 C/m . A proton (mass...

An infinitely long line of charge has linear charge density 5.00×10−12 C/m . A proton (mass 1.67×10−27 kg , charge e) is 14.5 cm from the line and moving directly toward the line at 2500 m/s . Calculate the proton’s initial kinetic energy. How close does the proton get to the line of charge? Please show how you got the answer so that I understand. :)

A)A straight, nonconducting plastic wire 7.50cm long carries a charge density of 130nC/m distributed uniformly along...

A)A straight, nonconducting plastic wire 7.50cm long carries a charge density of 130nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. -Find the magnitude and direction of the electric field this wire produces at a point 5.00cm directly above its midpoint. B) pick one of the two - electric field is directed upward - electric field is directed downward C) If the wire is now bent into a circle lying flat on the table, find the...

A straight, nonconducting plastic wire 7.50cm long carries a charge density of 130nC/m distributed uniformly along...

A straight, nonconducting plastic wire 7.50cm long carries a charge density of 130nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. Part A Find the magnitude and direction of the electric field this wire produces at a point 5.00cm directly above its midpoint. Part C If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 5.00cm directly above...