A hollow ball with radius R = 2 cm has a charge of -2 nC spread uniformly over its surface (see the figure). The center of the ball is at P1 = ⟨−3, 0, 0⟩cm. A point charge of 3 nC is located at P3 = ⟨5, 0, 0⟩ cm. (The diagram below is not drawn exactly to scale.) What is the net electric field at location P2 = ⟨0, 5, 0⟩ cm? E→ = N/C At a particular instant an electron is at location P2. What is the net electric force on the electron at that instant? F⇀ = N What is the direction of the net electric force on the electron? There is not enough information to determine the direction of the force The force is in the same direction as the electric field at P2 The force is at right angles to the direction of the electric field at P2 The force is opposite to the direction of the net electric field at P2
The slope of the 5.6 kN force F is specified as shown in the figure. Express F as a vector in terms of the unit vectors i and j. Assume a = 15, b = 6. Answer: F = (i + j) kN
A particle of charge +5.9 μC is released from rest at the point x = 86 cm on an x axis. The particle begins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 40 cm if (a) Q = +75 μC and (b) Q = −75 μC? (a) Number Units (b) Number Units
Three objects of equal mass m1 = m2 = m3 = 1.65 kg are located on the vertices of an equilateral triangle of length d = 3.65 m. A fourth mass m4 = 15.5 kg is at the center of the triangle. What is the net gravitational force on the mass m1 that is at the origin? Express your answer in vector form. F→net = N
Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (see Figure (a)). The magnitude of the electrostatic force acting on sphere 2 due to sphere 1 is F = 8.9 N. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (see Figure (b)), then to sphere 2 (see Figure (c)), and finally removed (see Figure (d)). What is the magnitude of the electrostatic force F′ that now acts on sphere 2? Number Units
Figure (a) shows an arrangement of three charged particles. Particles A and C are fixed on the x axis, but particle B can be moved along a circle centered on particle A. During the movement, a radial line between A and B makes an angle θ relative to the positive direction of the x axis (see Figure (b)). The curves in Figure (c) below give, for two situations, the magnitude Fnet of the net electrostatic force on particle A due to the other particles. That net force is given as a function of angle θ and as a multiple of a basic amount F0. For example on curve 1, at θ = 180∘, we see that Fnet = 2F0. (a) For the situation corresponding to curve 1, what is the ratio of the charge of particle C to that of particle B (including sign)? (b) For the situation corresponding to curve 2, what is that ratio? Assume d1 = d2 = d = 7.9 m. (a) Number Units (b) Number Units
A 8.4−kg rock and a 5.0×10−4−kg pebble are held near the surface of the earth. (a) Determine the magnitude of the gravitational force exerted on each by the earth. (b) Calculate the magnitude of the acceleration of each object when released. (a) Frock = Fpebble = (b) arock = apebble =
In Figure (a), particle A is fixed in place at x = −0.400 m on the x axis and particle B, with a mass of 4 kg, is fixed in place at the origin. Particle C (not shown) can be moved along the x axis, between particle B and x = ∞. Figure (b) shows the x component Fnet,x of the net gravitational force on particle B due to particles A and C, as a function of position x of particle C. The plot actually extends to the right, approaching an asymptote of −4.06×10−10 N as x→∞. What are the masses of (a) particle A and (b) particle C? (a) Number Units (b) Number Units
(a) Calculate the height (in m) of a cliff if it takes 2.33 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.20 m/s. m (b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? s
The drawing shows a uniform electric field that points in the negative y direction; the magnitude of the field is 7500 N/C. Determine the electric potential difference (a) VB−VA between points A and B, (b) VC−VB between points B and C, and (c) VA−VC between points C and A. (a) Number Units (b) Number Units (c) Number Units
Two small balls, each of mass 5.0 g are attached to silk threads 20 cm long, which in turn are tied to the same point in the ceiling. When the balls are given the same charge Q, the threads hang at 5.0∘ to the vertical, as shown below. What is the magnitude of Q? Q = nC
A thin plastic ring of radius R = 0.31 m is sprayed with electrically charged paint in a manner that half of the ring has a constant line charge density of +λ and the other half has constant line charge density of −λ, where λ = 4.6 mC/m. Part (a) Enter an expression for the magnitude of the electric field at the center of the ring. (Note: E is not zero even though the total charge on the ring is clearly zero.) E =
A charge of 5.0 nC is placed uniformly on a square sheet of nonconducting material of side length 19 cm in the yz plane. What is the surface charge density σ of the sheet? σ = nC/m2 What is the magnitude of the electric field E next to the sheet and proximate to the center of the sheet? E = kN/C What is the direction of the field?
Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.144 N when their center-to-center separation is 54.7 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 0.0372 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
In part (a) of the figure, particle 1 (of charge q1) and particle 2 (of charge q2) are fixed in place on an x axis, 12.00 cm apart. Particle 3 (of charge q3 = +8.00×10−19 C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force on it. In part (b) of the figure below gives the x component of that force versus the coordinate x at which particle 3 is placed. The scale of the x axis is set by xs = 12.00 cm. What are (a) the sign of charge q1 and (b) the ratio q2/q1? (a) (b)
A charge q = 5.50 μC sitting in a uniform electric field described by E = (3.00 i+2.00 j+2.20 k) V/m is moved from point A(x = 1.5, y = 1.0, z = 1.5)cm to point B(x = 1.5, y = 6.0, z = 6.5)cm along the path shown. Calculate the change in potential for this charge.
The figure shows a thin plastic rod of length L = 10.1 cm and uniform positive charge Q = 52.6 fC lying on an x axis. With V = 0 at infinity, find the electric potential at point P1 on the axis, at distance d = 2.01 cm from one end of the rod. Number Units
In the figure three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the rods are Q1 = +24 nC, Q2 = +3.7Q1, and Q3 = −6.0Q1. What is the net electric potential at the origin due to the rods? Number Units
(a) Two point charges totaling 9.00 μC exert a repulsive force of 0.200 N on one another when separated by 0.416 m. What is the charge (in μC) on each? smallest charge μC largest charge μC (b) What is the charge (in μC) on each if the force is attractive? smallest charge μC largest charge μC
The smiling face of the figure consists of three items: a thin rod of charge −4.50 μC that forms a full circle of radius 9.00 cm; a second thin rod of charge 3.00 μC that forms a circular arc of radius 6.00 cm, subtending an angle of 90∘ about the center of the full circle; an electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude 1.94×10−21 Gm. What is the net electric potential at the center? Number Units
The figure below shows a point-like charge q = 8.4 μC held at point A, distance a = 83 cm away from the end of a thin insulating rod of length c = 91.5 cm that carries uniform linear charge density λ = 0.378 μC/cm. How much work W needs to be done to move this charge q to point B, also shown in the figure, which is distance b = 3.8 cm away from the end of the rod? : W = J.
Consider the circuit shown in the figure. Before the two capacitors were inserted into the circuit, they were fully charged by a 21.0 V battery. Imagine that the switch is now closed. (a) After a time interval of 1.70 ms, what is the value of the remaining charge (in μC) on the 3.00 μF capacitor? μC (b) After a time interval of 1.70 ms, what is the value of the remaining charge (in μC) on the 2.00 μF capacitor? μC (c) What is the current (in mA) in the resistor at this time? mA
In Figure (a) particles 1 and 2 have charge 42.0 μC each and are held at separation distance d = 4.50 m. (a) What is the magnitude of the electrostatic force on particle 1 due to particle 2? In Figure (b), particle 3 of charge 42.0 μC is positioned so as to complete an equilateral triangle. (b) What is the magnitude of the net electrostatic force on particle 1 due to particles 2 and 3? (a) (b) (a) Number Units (b) Number Units
Consider the circuit shown in the figure below, where C1 = 8.00 μF, C2 = 6.00 μF, and ΔV = 18.0 V. Capacitor C1 is first charged by closing switch S1. Switch S1 is then opened, and the charged capacitor is connected to the uncharged capacitor by closing S2. (a) Calculate the initial charge (in μC) acquired by C1. (Round your answer to at least one decimal place.) μC (b) Calculate the final charge (in μC) on each capacitor. (Round your answers to at least the nearest integer.) Q1 = μC Q2 = μC (c) What If? After a very long time, switch S1 is also closed. By what amount does the charge on the second capacitor change after S1 has been closed for a very long time? (Give your answer in μC.) μC
A charge of +3.00 μC is located at the origin, and a second charge of −2.00 μC is located on the xy-plane at the point (50.0 cm, 40.0 cm). Determine the magnitude F of the electric force exerted by the −2.00 μC charge on the +3.00 μC charge. F = N Determine the direction of electric force exerted by the −2.00 μC charge on the +3.00 μC charge, expressed as an θ = angle θ measured counterclockwise from the positive x-axis.
Consider the figure with a symmetrical arrangement of charges, in which qa = qb = +7.55 μC, qc = qd = −7.55 μC, and q is positive. Use k = 1/(4πϵ0) = 8.99×109 N⋅m2 /C2 for the Coulomb constant. Using the symmetry of the arrangement, determine the direction of the force on charge q. up down left right up and left up and right down and left down and right Calculate the magnitude of the force F on the charge q given that the square is 10.70 cm on a side and q = 1.55 μC. F = N
1 D Kinematics with non-constant acceleration 7. A car is driving towards a red light (at x0 = 0 and t0 = 0) with an initial speed of Vo. The acceleration of the car is a = {0 t < t1 −B(t−t1) t1 < t < t2, where the car's velocity is in the positive direction, B is a constant, and the car comes to a halt at time t2. a. What are the units of B? b. Without explicit calculation, first sketch the position, velocity, and acceleration vs. time graphs. c. Now calculate the velocity and position of the car as functions of time. Compare to your sketches. d. Determine t2, the time when the car stops. Answer: If t1 = 0.5 s, Vo = 18 m/s, and B = 16 (units?), you should calculate t2 = 2 s.
A ball is released from rest from the twentieth floor of a building. After 1 s, the ball has fallen one floor such that it is directly outside the nineteenth-floor window. The floors are evenly spaced. Assume air resistance is negligible. What is the number of floors the ball would fall in 3 s after it is released from the twentieth floor? A 3 floors or less B 4 to 6 floors (C) 7 to 10 floors (D) 11 floors or more
The magnitude of the electrostatic force between two identical ions that are separated by a distance of 6.10×10−10 m is 139.5×10−9 N. (a) What is the charge of each ion? (b) How many electrons are "missing" from each ion (thus giving the ion its charge imbalance)? (a) Number Units (b) Number Units
A charge of -2.65 nC is placed at the origin of an xy-coordinate system, and a charge of 2.40 nC is placed on the y axis at y = 3.50 cm. Part A If a third charge, of 5.00 nC, is now placed at the point x = 3.50 cm, y = 3.50 cm find the x and y components of the total force exerted on this charge by the other two charges. Express answers numerically separated by a comma. Fx, Fy = N Submit Request Answer Part B Find the magnitude of this force. Submit Request Answer Part C Find the direction of this force. θ = below the +x axis
Earth's atmosphere is constantly bombarded by cosmic ray protons that originate somewhere in space. If the protons all passed through the atmosphere, each square meter of Earth's surface would intercept protons at the average rate of 1600 protons per second. What would be the electric current in amperes intercepted by a 18×107 km2 area on the planet? Number Units
If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of -5.30 μC. (a) How many electrons are transferred between you and the cat? You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a faucet, a painful spark can suddenly appear as your fingers near the faucet. (b) In that spark, do electrons flow from you to the faucet or vice versa? (c) Just before the spark appears, do you induce positive or negative charge in the faucet? (d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark, from faucet to the cat or vice versa? (a) Number Units (b) (c) (d)
The 0.45 kg soccer ball is 1 m above the ground when it is kicked upward at 12 m/s. Determine the magnitude of the ball's velocity when it is 4 m above the ground. Obtain the answer by placing the datum (a) at the level of the ball's initial position and (b) at ground level.
In the figure particles 1 and 2 of charge q1 = q2 = +17.60×10−19 C are on a y axis at distance d = 18.6 cm from the origin. Particle 3 of charge q3 = +38.40×10−19 C is moved gradually along the x axis from x = 0 to x = +7.45 m. At what values of x will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes? (a) Number Units (b) Number Units (c) Number Units (d) Number Units