Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities σ1, σ2, σ3 and σ4 on their surfaces, as shown in the following figure (Figure 1). These surface charge densities have the values σ1 = −6.60 μC/m2, σ2 = 5.00 μC/m2, σ3 = 1.60 μC/m2, and σ4 = 4.00 μC/m2. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets. Figure 1 of 1 Part A What is the magnitude of the electric field at point A, 5.00 cm from the left face of the left-hand sheet? Express your answer with the appropriate units. Submit Request Answer Part B What is the direction of the electric field at point A, 5.00 cm from the left face of the left-hand sheet? to the left. to the right. upwards. downwards. Part C What is the magnitude of the electric field at point B, 1.25 cm from the inner surface of the right-hand sheet? Express your answer with the appropriate units. Submit Request Answer Part D What is the direction of the electric field at point B, 1.25 cm from the inner surface of the right-hand sheet? to the left. to the right. upwards. downwards. Part E What is the magnitude of the electric field at point C, in the middle of the right-hand sheet? Express your answer with the appropriate units. Submit Request Answer Part F What is the direction of the electric field at point C, in the middle of the right-hand sheet? to the left. to the right. upwards. downwards. Submit Request Answer
You have a circular ring of mass 100 kg. 5 of your friends try to pull it in different directions as shown. What is the NET force they are pulling with? Note that F1 = 8.6, F2 = 6.4, and F3 = 10.2. F2 makes an angle of 45∘ with the x -axis. What is the net force in newtons? Fnet = Problem 2: (14% of Assignment Value)
Four identical charged particles (q = +10.3 μC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 60.6 cm and W = 16.0 cm. (a) Calculate the magnitude of the total electric force exerted on the charge at the lower left corner by the other three charges. N (b) Calculate the direction of the total electric force exerted on the charge at the lower left corner by the other three charges. ∘ (counterclockwise from the +x-axis)
What must be the distance in meters between point charge q1 = 34.2 μC and point charge q2 = −66.0 μC for the electrostatic force between them to have a magnitude of 7.45 N? Number Units
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.108 N when their center-to-center separation is 55.9 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0357 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other? (Assume the negative charge has smaller magnitude) (a) Number Units (b) Number Units
A block of mass m = 8, 3 kg slides on a rough surface and moves toward a spring with a spring constant k, as shown in the figure below. When the block is d = 20 m away from the spring, it has a velocity of v = 16, 7 m/s. When the block momentarily stops, it has compressed the spring by x = 34 cm. If the coefficient of kinetic friction between the block and the surface below is μk = 0, 32, determine the spring constant, k = ? Provide your answer zero decimal places. Take g = 9.80 m/s2.
Consider the following figure. The three forces F1, F2, and F3 are acting at the same point P as shown in the figure. (a) Find the resultant force acting at P. (Round your answers to two decimal places.) (b) Find the angle the resultant force makes with the positive x-axis. (use a positive value and round your answer to two decimal places.) angle
A 0.500 kg mass is attached to a spring of constant 150 N/m. A driving force F(t) = (3N)cos(ωt) is applied to the mass, and the damping coefficient b is 6.00 Ns/m. What is the amplitude (in cm) of the steady-state motion if ω is equal to half of the natural frequency ω0 of the system? Enter a number with two digits behind the decimal point.
From t = 0 to t = 4.03 min, a man stands still, and from t = 4.03 min to t = 8.06 min, he walks briskly in a straight line at a constant speed of 2.70 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg in the time interval 1.00 min to 5.03 min? What are (c) vavg and (d) aavg in the time interval 2.00 min to 6.03 min? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
An ice hockey puck of mass 170 g enters the goal with a momentum of < 0, 0, −6.4 > kg⋅m/s, crossing the goal line at location < 0, 0, −25 > m relative to an origin in the center of the rink. The puck had been hit by a player 0.6 s before reaching the goal. What was the location of the puck when it was hit by the player, assuming negligible friction between the puck and the ice? (Note that the ice surface lies in the xz plane. Express your answer in vector form.) r→i = < > m
For this question (see the simulation) set charge 1 to 3 μC. By adjusting the charge of charge 2 only, what is the largest magnitude electric field you can obtain at the following locations? Assume all numbers stated in this problem are accurate to three significant figures. Try to solve the problems using principles of physics, and then use the simulation to check your answers. (a) Under these conditions, find the largest magnitude electric field obtainable using the simulation at the point X = 0.12 m, Y = 0 m. (b) Under these conditions, find the largest magnitude electric field obtainable using the simulation at the point X = 0 m, Y = 0.86 m. (c) Under these conditions, find the largest magnitude electric field obtainable using the simulation at the point X = 0 m, Y = 0.16 m. (a) Number Units (b) Number Units (c) Number Units
A pair of infinite parallel planes are separated by a distance d, with one above the other. The top plane has a uniform charge density σ. The bottom plane has a uniform charge density −σ. a. Determine the electric field everywhere. [Note that there is no slab between the planes for part a.] b. An infinite conducting slab is placed between the two planes with top and bottom faces parallel to the two planes and without touching the two planes. Determine the induced charge densities on the top and bottom of the conducting slab.
Consider two identical conducting spheres placed on identical nonconductive mounts. Initially, both spheres have no net charge. Sphere #2 is then connected to a +3000 volt source, acquiring a positive net charge. Sphere #1 is placed near Sphere #2 (without touching it). State the sign of the charge at points a, b, and c. Scath the figures explaining the charge distributions and give detailed explanation. (10 pts)
A charge of q1 = −3.3 nC is located at (x1, y1) = (4.7 m, −9.8 m). A charge of q2 = 7.9 nC is located at (x2, y2) = (−1 m, −4.3 m). In newtons per coulomb, what is the x-component the electric field at the origin due to q1 and q2? Use k = 8.99×109 N⋅m2 C.
A ball of charge q = 2.7 C and mass m = 5.4 kg is placed in a uniform electric field of strength |E| = 4 N/C. How many meters does the charge travel in Δt = 2.3 seconds?
Four charges −5×10−9 C at (0 m, 0 m), 6×10−9 C at (−4 m, 4 m), −5×10−9 C at (5 m, 1 m), and −8×10−9 C at (−2 m, −3 m), are arranged in the (x, y) plane as shown. Find the magnitude of the resulting force on the -5 nC charge at the origin. The Coulomb constant is 8.98755×109 N⋅m2 /C2. Answer in units of N. Answer in units of N. part 2 of 2 What angle does the resultant force on the -5 nC charge at the origin make with the positive x axis? Quadrant I lies between 0∘ and 90∘, quadrant II between between 90∘ and 180∘, etc. Answer in units of ∘. Answer in units of ∘.
An infinite sheet of current lying in the yz plane carries a surface current of linear density Js. The current is in the positive z direction, and Js represents the current per unit length measured along the y axis. Figure P30.34 is an edge view of the sheet. Prove that the magnetic field near the sheet is parallel to the sheet and perpendicular to the current direction, with magnitude μ0Js/2. Figure P30.34
The car is originally at rest. It then increases its speed at v˙ = (0.05 t2) ft/s2, where t is in seconds. Calculate the following once it has traveled a tenth of a mile: a. The tangential and normal components of its velocity and acceleration b. The ı^ and ȷ^ components of its velocity and acceleration c. The magnitudes of its velocity and acceleration
An object with mass m = 37.9 kg is supported by two ropes, as shown. A coordinate system is provided. A horizontal applied force of magnitude F acts, through the horizontal rope, on the object. The other rope has tension T and makes an angle of φ = 21∘ with the vertical. Part (a) Write an expression for the y component of the net force, ΣFy. ΣFy = Part (b) Write an expression for the x component of the net force. ΣFx ΣFx =
At a particular instant a proton is at the origin, moving with velocity < 5×104, −9×104, −9×104 > m/s Part 1 (a) At this instant, what is the electric field at location < 3×10−3, 3×10−3, 3×10−3 > m due to the proton? (Express your answer in vector form.) E→ = < > N/C Part 2 (b) At this instant, what is the magnetic field at the same location due to the proton? (Express your answer in vector form.) B→ = < > T
Fields of an electron At a particular instant a proton is at the origin, moving with velocity < 6×104, −3×104, −5×104 > m/s. At this instant: (a) What is the electric field at location < 4×10−3, 2×10−3, 3×10−3 > m, due to the proton? E→ = < > N/C (b) What is the magnetic field at the same location due to the proton? B→ = < > T
A woman on a bridge 105 m high sees a raft floating at a constant speed on the river below. She drops a stone from rest in an attempt to hit the raft. The stone is released when the raft has 4.75 m more to travel before passing under the bridge. The stone hits the water 2.09 m in front of the raft. Find the speed of the raft. Number Units
An object moves in one dimension along the x-axis. At time t = 0, the object is located at position x = 1 m and has a velocity v = 1 m/s. The object's acceleration varies as a = 3 t, where a is in m/s2 and t is time in seconds. A student incorrectly derives the equation for the object's position as x = 12 t3+1, where x is in meters. Which of the following describes a possible error that could have resulted in the incorrect equation? (A) The student's equation does not account for the initial position of the object. (B) The student's equation does not account for the initial velocity of the object. (C) The student's equation does not substitute a = 3 t in the 12 at2 term. (D) The student's equation should not have a +1 term, as integrating the acceleration function twice yields x = 12 t3
A woman on a bridge 108 m high sees a raft floatingat a constant speed on the river below. She drops a stone from rest in an attempt to hit the raft. The stone is released when the raft has 9.94 m more to travel before passing under the bridge. The stone hits the water 4.59 m in front of the raft. Find the speed of the raft. Number Units