Concept explainers
a.
The magnitude and the direction of the electric field at
The electric field
Given:
The charges are placed as shown in the figure. The first plane at
The surface charge densities are
Formula Used:
Electric field
E is the electric field.
The resultant electric field at point is
Calculations:
The resultant electric field at point is
Electric field at point 1 due to sphere.
As the point is inside the sphere the electric field is zero.
Electric field at point 1 due to plane 1
Substituting values
The electric field at point 1 due to plane 2.
Substituting in the equation
The resultant electric field at point is
Substituting
The magnitude of the electric field is
Direction:
Conclusion:
The electric field
b.
The magnitude and the direction of the electric field at
The electric field
Given:
The charges are placed as shown in the figure. The first plane at
The surface charge densities are
Formula Used:
Electric field
E is the electric field.
The resultant electric field at point is
Calculations:
The resultant electric field at point is
Electric field at point 1 due to sphere.
Where
Electric field at point 1 due to plane 1
Substituting values in the formula
The electric field at point 1 due to plane 2.
Substituting in the equation
The resultant electric field at point is
Substituting
The magnitude of the electric field is
Direction:
Conclusion:
The electric field
a.
Answer to Problem 77P
The electric field
Explanation of Solution
Given:
The charges are placed as shown in the figure. The first plane at
The surface charge densities are
Formula Used:
Electric field
E is the electric field.
The resultant electric field at point is
Calculations:
The resultant electric field at point is
Electric field at point 1 due to sphere.
As the point is inside the sphere the electric field is zero.
Electric field at point 1 due to plane 1
Substituting values
The electric field at point 1 due to plane 2.
Substituting in the equation
The resultant electric field at point is
Substituting
The magnitude of the electric field is
Direction:
Conclusion:
The electric field
b.
The magnitude and the direction of the electric field at
The electric field
Given:
The charges are placed as shown in the figure. The first plane at
The surface charge densities are
Formula Used:
Electric field
E is the electric field.
The resultant electric field at point is
Calculations:
The resultant electric field at point is
Electric field at point 1 due to sphere.
Where
Electric field at point 1 due to plane 1
Substituting values in the formula
The electric field at point 1 due to plane 2.
Substituting in the equation
The resultant electric field at point is
Substituting
The magnitude of the electric field is
Direction:
Conclusion:
The electric field
b.
Answer to Problem 77P
The electric field
Explanation of Solution
Given:
The charges are placed as shown in the figure. The first plane at
The surface charge densities are
Formula Used:
Electric field
E is the electric field.
The resultant electric field at point is
Calculations:
The resultant electric field at point is
Electric field at point 1 due to sphere.
Where
Electric field at point 1 due to plane 1
Substituting values in the formula
The electric field at point 1 due to plane 2.
Substituting in the equation
The resultant electric field at point is
Substituting
The magnitude of the electric field is
Direction:
Conclusion:
The electric field
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Chapter 22 Solutions
Physics for Scientists and Engineers
- A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge Q. Concentric with this sphere is an uncharged, conducting, hollow sphere whose inner and outer radii are b and c as shown in Figure P19.75. We wish to understand completely the charges and electric fields at all locations. (a) Find the charge contained within a sphere of radius r a. (b) From this value, find the magnitude of the electric field for r a. (c) What charge is contained within a sphere of radius r when a r b? (d) From this value, find the magnitude of the electric field for r when a r b. (e) Now consider r when b r c. What is the magnitude of the electric field for this range of values of r? (f) From this value, what must be the charge on the inner surface of the hollow sphere? (g) From part (f), what must be the charge on the outer surface of the hollow sphere? (h) Consider the three spherical surfaces of radii a, b, and c. Which of these surfaces has the largest magnitude of surface charge density?arrow_forwardA spherical conductor of radius 0.330 m has a spherical cavity of radius 0.120 m at its center. The conductor carries a total charge of -6.00 nC; in addition, at the center of the spherical cavity is a point charge of +4.00 nC. (a) Find the total charge on the surface of the cavity. (b) Find the total charge on the surface of the conductor.arrow_forwardAn infinitely long cylindrical conducting shell of outer radius r1 = 0.10 m and inner radius r2 = 0.08 m initially carries a surface charge density σ = -0.45 μC/m2. A thin wire, with linear charge density λ = 1.2 μC/m, is inserted along the shells' axis. The shell and the wire do not touch and there is no charge exchanged between them. What is the new surface charge density, in microcoulombs per square meter, on the inner surface of the cylindrical shell? What is the new surface charge density, in microcoulombs per square meter, on the outer surface of the cylindrical shell? Enter an expression for the magnitude of the electric field outside the cylinder (r > 0.1 m), in terms of λ, σ, r1, r, and ε0.arrow_forward
- A charge -300e is uniformly distributed along a circular arc of radius 4.00 cm, which subtends an angle of 40°. What is the linear charge density along the arc? A charge -300e is uniformly distributed over one face of a circular disk of radius 2.00 cm. What is the surface charge density over that face? A charge -300e is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? A charge -300e is uniformly spread through the volume of a sphere of radius 2.00 cm. What is the volume charge density in that sphere?arrow_forward(a) Figure (a) shows a nonconducting rod of length L = 5.40 cm and uniform linear charge density λ = +4.41 pC/m. Take V = 0 at infinity. What is V at point P at distance d = 9.30 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 4.41 pC/m. With V= 0 at infinity, what is V at P? (a) Number i (b) Number i P ‡ ‡ ‡ ‡ + + + +‡‡ ‡ ‡‡ L/2 L/2 Units Units [+ + + ++++G ·L/2 L/2-arrow_forwardA charge -300e is uniformly distributed along a circular arc of radius 4.00 cm, which subtends an angle of 40o.What is the linear charge density along the arc? (b) A charge 300e is uniformly distributed over one face of a circular disk of radius 2.00 cm. What is the surface charge density over that face? (c) A charge -300e is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? (d) A charge -300e is uniformly spread through the volume of a sphere of radius 2.00 cm. What is the volume charge density in that sphere?arrow_forward
- Consider an infinite line of charge, with linear charge density +3.5 x 10-12 C/m. This line of charge is parallel to the z-axis and intersects the x-y plane on the x axis at x = -6.7 m. Now consider a second infinite line of charge, with linear charge density +2 x 10-12 C/m. This line of charge is also parallel to the z-axis and intersects the x-y plane on the x axis at x = +14.3 m. Calculate the magnitude of electric field, in N/C, at the origin. Use ε 0 = 8.9 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forwardCharge is placed on the surface of a 2.7-cm radius isolated conducting sphere. The surface charge density is uniform and has the value 6.9x10-6 C/m². The total charge on the sphere is: O 6.3x10-8 C O 4.7x10-8 C O 2.1x10-8 C O 5.6x10-8 Carrow_forwardAn infinite sheet of charge is located in the y-z plane at x = 0 and has uniform charge denisity o1 = 0.62 µC/m2. Another infinite sheet of charge with uniform charge density o7 = -0.29 µC/m? is located at x = c = 33 cm.. An uncharged infinite conducting slab is placed halfway in between these sheets ( i.e., between x = 14.5 cm and x 3 18.5 сm). a/2 a/2| a/2 1) What is Ex(P), the x-component of the electric field at point P, located at (x,y) = (7.25 cm, 0)? N/C Submit 2) What is oa, the charge density on the surface of the conducting slab at x = 14.5 cm? µC/m? Submit 3) What is V(R) - V(P), the potentital difference between point P and point R, located at (x,y) = (7.25 cm, -18.5 cm)? Submit 4) What is V(S) - V(P), the potentital difference between point P and point S, located at (x,y) = (25.75 cm, -18.5 cm)? Submit + 5) What is Ex(T), the x-component of the electric field at point T, located at (x,y) (40.25 сm, -18.5 ст)? N/C Submitarrow_forward
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