Concept explainers
(a)
The electric field at x = 5.00 cm.
Answer to Problem 16PE
The electric field at x = 5.00 cm is
Explanation of Solution
Given:
Point charges located at 3.00, 8.00 and 11.0 cm along the x -axis.
Formula used:
Electric field in point P distanced di from n charges on a line is given with
Where positive sign is taken for charges left to the point P and negative for charges right to P.
Calculation:
Conclusion:
The electric field at x = 5.00 cm is
(b)
To Find:
The position between 3.00 and 8.00 cm where the total electric field the same as that for − 2q alone.
Answer to Problem 16PE
The position is 7 cm.
Explanation of Solution
Given:
Point charges located at 3.00, 8.00 and 11.0 cm along the x -axis.
Calculation:
The charges will cancel out at the mid-point of
So, we get
Conclusion:
Thus, the position is at 7 cm.
(c)
Whether the electric field between 0.00 and 8.00 cmbe zero.
Answer to Problem 16PE
Electric filed will never be zero.
Explanation of Solution
Given:
Point charges located at 3.00, 8.00 and 11.0 cm along the x -axis.
Calculation:
Note that such cancellation can't happen between a
which is not possible.
In other words, when it reaches 0 after continuously dropping in some direction, electric field will change direction.
Since
Which means it points to the left, so E = 0 can't happen neither it can happen between
Conclusion:
Electric field will never be zero.
(d)
To Find: where the electric field most rapidly approaches zero for very large positive or negative values of x in case (a) and (b).
Answer to Problem 16PE
Electric field of configuration (a) drops more rapidly.
Explanation of Solution
Given:
Point charges located at 3.00, 8.00 and 11.0 cm along the x -axis.
Calculation:
Total charge in (a) is zero, while total charge in (b) is not zero.
Looked from infinity, those charges may be considered emerging from the same point, so electric field in (a) will drop more rapidly.
Conclusion:
Thus, Electric field of configuration (a) drops more rapidly
(e)
Find the position to the right of 11.00 cm where the total electric field is zero, other than at infinity.
Answer to Problem 16PE
The position to the right of 11.00 cm where the electric field is zero other than infinity is 30.872 cm.
Explanation of Solution
Given info:
Point charges located at 3.00, 8.00 and 11.0 cm along the x -axis.
Calculation:
After cancelling some constants, we can obtain an equation,
This after some algebraic manipulation converts to,
With one real solution, x = 19.872 cm. since x denotes distance from the rightmost charge, coordinate of such point in the system given is,
Conclusion:
Thus, the position to the right of 11.00 cm where the electric field is zero other than infinity is 30.872 cm.
Want to see more full solutions like this?
Chapter 18 Solutions
COLLEGE PHYSICS
- Is it possible for a conducting sphere of radius 0.10 m to hold a charge of 4.0 C in air? The minimum field required to break down air and turn it into a conductor is 3.0 106 N/C.arrow_forward(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that qa= 1.00C and qc=qd= +1.00 C. (b) Calculate the magnitude of the electric field at the location of q, given that the square is 5.00 cm on a side.arrow_forward(a) Find the electric field at x = 5.00 cm in (a), given that q = 1.00 μC . (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for –2q alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidlyapproach zero and why? (e) At what position to the right of 11.0 cm is the total electric field zero, other than at infinity?(Hint: A graphing calculator can yield considerable insight in this problem.)arrow_forward
- Find the electric field at P in the figure shown below. (Take r = 1.6 m and 0 = 44°. Measure the angle counterclockwise from the positive x-axis.) magnitude O direction P r 9= 10×10-⁹Carrow_forwardProblem 3: The electric field in a certain region is given by the function E = Ak cos (kx) cos (by) i – Ab sin (kx) sin (by) where A = 18.06 N-m/C, k = 0.702 m ¹, and b = 1.29 m¹. The points in the figure use the values 1 1.5 m and u₁= 3.36 m. Part (a) What is the change in electric potential, in volts, from point (0, 0) to point (x₁, 0)? V(x₁,0) - V(0, 0) = Part (b) What is the change in potential, in volts, from point (x₁, 0) to point (x₁.y₁)? V(x1.₁) - V(x₁.0)=1 V V V (0,y₁) Part (c) What is the change in potential, in volts, from point (0, 0) to point (₁. ₁), along the path that passes through (x₁, 0)? V(x₁, y₁) - V(0, 0) = (0,0) (x₁₂V₁) (x₁,0)arrow_forwardAn electric dipole is formed from two charges ± q, spaced 5.24mm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x,y)= (0.00cm, 58.9cm) is 400.0N/C. What is the charge q? 2077N/C Submit Answer Incompatible units. No conversion found between Tries 0/10 "N/C" and the required units. Submit Answer What is the electric field's magnitude at the point (x,y)= (58.9cm, 0.00cm)? 2077N/C Previous Tries Incorrect. Tries 1/10 Previous Triesarrow_forward
- What is the magnitude of the electric field produced by a charge of magnitude 4.70 μCμC at a distance of (a) 1.00 mm and (b) 3.00 mm?arrow_forwardA thick insulating spherical shell of inner radius a=2.1R and outer radius b=7.8R has a uniform charge density p. pR What is the magnitude of the electric field at r=9.6 R ? Express your answer using one decimal place in units of €0arrow_forwardConsider the following figure. (If you need to use ∞ or -∞, enter INFINITY or -INFINITY, respectively.) (a) (b) 0 -2q +9 5 5 +9 -29 +3q 10 10 +q x (cm) x (cm) -9 (a) Find the total electric field in N/C at x = 1.00 cm in part (b) of the figure above given that q = 5.00 nC. N/C (b) Find the total electric field in N/C at x = 10.70 cm in part (b) of the figure above. (Include the sign of the value in your answer.) N/C (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge, etc., and what will its value(s) be? Use the following as necessary: q.)arrow_forward
- This question checks that you can use the formula of the electric field due to a long, thin wire with charge on it. The field due to an infinitely long, thin wire with linear charge E = 12X Απερ η density is Imagine a long, thin wire with a constant charge per unit length of -2.3×10 C/m. What is the magnitude of the electric field at a point 10 cm from the wire (assuming that the point is much closer to the wire's nearest point than to either of its ends)? Give your answer in units of kN/C. -7arrow_forward+x 91 r2 92 P Find the net electric field in N/C at point P, where q1 = (-7.8480x10^0) nC, r1 = (3.6940x10^-1) metres, q2 = (4.25x10^0) nC and r2 = (5.491x10^-1) metres. You do not need to include a unit vector in your answer, but must include a minus sign if the field direction is in the negative x direction. %3Darrow_forwardYou are working as an intern for a meteorological laboratory. You are out in the field taking measurements with a device that measures electric fields. You measure the electric field in the air immediately above the Earth's surface to be 139 N/C directed downward. (Assume the radius of the Earth is 6.37 x 106 m.) (a) Determine the surface charge density (in C/m²) on the ground. C/m? (b) Imagine the surface charge density is uniform over the planet. Determine the charge (in C) of the whole surface of the Earth. (e) Determine the Earth's electric potential (in V) due to the charge found in (b). V (d) Determine the difference in potential (in V) between the head and the feet of a person 1.50 m tall. (Ignore any charges in the atmosphere.) Varrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning