Given the quantities a = 5.3 m, b = 1.3 s, c = 52 m/s, what is the value of the quantity d = a3 cb2? Number Units
The figure shows three circular arcs centered at the origin of a coordinate system. On each arc, the uniformly distributed charge is given in terms of Q = 4.88 μC. The radii are given in terms of R = 9.04 cm. What are the (a) magnitude and (b) direction (relative to the positive x direction) of the net electric field at the origin due to the arcs? (a) Number Units (b) Number Units
When chasing a hare along a flat stretch of ground, a greyhound leaps into the air at a speed of 10.2 m/s, at an angle of 30.0∘ above the horizontal. (a) What is the range of his leap and (b) for how much time is he in the air? (a) Number Units (b) Number Units
An electric dipole consists of charges +2e and −2e separated by 0.69 nm. It is in an electric field of strength 3.9×106 N/C. Calculate the magnitude of the torque on the dipole when the dipole moment is (a) parallel to, (b) perpendicular to, and (c) antiparallel to the electric field. (a) Number Units (b) Number Units (c) Number Units
Charge Q1 = 17.91 mC is placed R = 35.65 cm to the left of charge Q2 = 80.73 mC, as shown in the figure. Both charges are held stationary. Point A is located R3 = 10.70 cm to the right of Q1. A particle with a charge of q = −6.551 μC and a mass of 31.31 g is placed at rest at a distance R2 = 32.09 cm above Q2. If the particle were to be released from rest, calculating its exact path would be a challenging problem. However, it is possible to make some definite predictions about the future motion of the particle If the path of the particle were to pass through point A, what would be its speed vA at that point?
In the figure below, suppose the charge q2 can be moved left or right from its shown location, along the line connecting the charges q1 and q3, rather than sitting at a distance d from each. You will find where it experiences a net electric force of zero. (The charges q1 and q3 remain separated by a fixed distance of 2d = 44 cm.) (Note that all charges are expressed in terms of the common multiple "q".) a.) Concept: Where will q2 experience a net electric force of zero? b.) Calculate: Find the exact distance where this occurs. cm, away from q1.
A distance of 4.00 cm is measured between two adjacent nodes of a standing wave on a 16.0 cm -long string. (a) In which harmonic number n is the string vibrating? (b) Find the frequency (in Hz) of this harmonic if the string has a mass of 1.45×10−2 kg and a tension of 855 N. Hz
In the arrangement shown in the figure below, an object of mass m = 2.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.0 m. (Ignore the mass of the vertical section of the cord.) (a) When the vibrator is set to a frequency of 140 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord? kg/m (b) How many loops (if any) will result if m is changed to 4.50 kg? (Enter 0 if no loops form.) loops (c) How many loops (if any) will result if m is changed to 14 kg? (Enter 0 if no loops form.) loops
In the figure four particles are fixed along an x axis, separated by distances d = 3.50 cm. The charges are q1 = +4e, q2 = −e, q3 = +e, and q4 = +12e, with e = 1.60×10−19 C. What is the value of the net electrostatic force on (a) particle 1 and (b) particle 2 due to the other particles? (a) Number Units (b) Number Units
The figure is a section of a conducting rod of radius R1 = 1.30 mm and length L = 13.40 m inside a thin-walled coaxial conducting cylindrical shell of radius R2 = 11.3R1 and the (same) length L. The net charge on the rod is Q1 = +3.50×10−12 C; that on the shell is Q2 = −2.08Q1. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 2.08R2? What are (c) E and (d) the direction at r = 5.16R1? What is the charge on the (e) interior and (f) exterior surface of the shell? (a) Number Units (b) (c) Number Units (d) (e) Number Units (f) Number Units
Four identical charged particles (q = +11.0 μC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 64.8 cm and W = 16.6 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)
You are in a hot-air balloon that, relative to the ground, has a velocity of 5.22 m/s in a direction due east. You see a hawk moving directly away from the balloon in a direction due north. The speed of the hawk relative to you is 1.11 m/s. What are (a) the magnitude and (b) direction of the hawk's velocity relative to the ground? Express the directional angle relative to due east. (a) Number Units (b) Number Units
The position of an object moving along an x axis is given by x = 3.03t − 4.24t2 + 1.05t3, where x is in meters and t in seconds. Find the position of the object at the following values of t : (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity from t = 2 s to t = 4 s? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
Three point-like charges are placed at the corners of an equilateral triangle as shown in the figure, a = 60.0 cm. Find the magnitude of the electric force exerted on the charge q3. Let q1 = −2.50 μC, q2 = +3.10 μC, and q3 = −3.60 μC. N
A 2.80 kg object is subjected to three forces that give it an acceleration a→ = (4.50 m/s2)i^ + (6.20 m/s2)j^. If two of the three forces are F→1 = (29.0 N)i^ + (11.0 N)j^ and F→2 = (15.0 N)i^ + (7.90 N)j^, find (a) the x component and (b) the y component of the the third force. (a) Number Units (b) Number Units
A large positively charged object with charge q+ = 3.25 μC is brought near a negatively charged plastic ball suspended from a string of negligible mass. The suspended ball has a charge of q− = −46.3 nC and a mass of 17.5 g. What is the angle θ that the string makes with the vertical when the positively charged object is 17.5 cm from the θ = suspended ball? The positively charged object is at the same height as the suspended ball.
A line of positive continuous charge is formed into a semicircle of radius R = 68 cm depicted below. The total charge of this semicircle Q = 10 μC. This charge, however, is distributed not uniformly along the semicircle but with the angle-dependent linear charge density λ(θ) = λ0cosθ. What is the value of parameter λ0? λ0 = μC/cm. Find now the electric field at the central point P in terms of its Ex and Ey components (with respect to the axes shown in the figure). Ex = N/C Ey = N/C
The figure shows two parallel nonconducting rings with their central axes along a common line. Ring 1 has uniform charge q1 and radius R; ring 2 has uniform charge q2 and the same radius R. The rings are separated by a distance 3.00 R. The ratio of the electric field magnitudes of Ring 1 and Ring 2 at point P on the common line is 2.16. What is the ratio of charge magnitudes q1/q2? Number Units
The figure below shows a thin rod of length L = 3.5 m with total charge Q = 120 nC. Find the electric field E→ at distance x = 0.7 m from the end of the rod. Give your answer in component form and in units of V/m. E→ = i^ + j^
Location A is 2.70 m to the right of a point charge q. Location B lies on the same line and is 4.60 m to the right of the charge. The potential difference VB−VA = 42.0 V. What is the magnitude and sign of the charge? Number Units
In the figure two curved plastic rods, one of charge +q and the other of charge −q, form a circle of radius R = 3.75 cm in an xy plane. The x axis passes through both of the connecting points, and the charge is distributed uniformly on both rods. If q = 13.0 pC, what is the magnitude of the electric field produced at P, the center of the circle? Number Units
A 3.4 μC point charge is placed in an external uniform electric field that has a magnitude of 32000 N/C. At what distance from the charge is the net electric field zero? Number Units
The drawings show three charges that have the same magnitude but may have different signs. In all cases the distance d between the charges is the same. The magnitude of the charges is |q| = 9.7 μC, and the distance between them is d = 4.1 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings. (a) F = (b) F = (c) F =
Two test charges are located in the x−y plane. If q1 = −3.200 nC and is located at x1 = 0.00 m, y1 = 1.2000 m, and the second test charge has magnitude of q2 = 3.600 nC and is located at x2 = 1.300 m, y2 = 0.450 m, calculate the x and y components, Ex and Ey, of the electric field E→ in component form at the origin, (0, 0). The Coulomb force constant is 1/(4πϵ0) = 8.99×109 N⋅m2/C2 Ex = N/C Ey = N/C
You want to calculate the electric field at location ⟨0.5, −0.6, −0.5⟩m, due to a particle with charge +8.0 nC located at ⟨−0.1, −0.7, −0.2⟩m. (a) What is the source location? (Express your answer in vector form.) r→source = m (b) What is the observation location? (Express your answer in vector form.) r→obs = m (c) What is the vector r→ that points from the source location to the observation location? (Express your answer in vector form.) r→ = m (d) What is |r→|? m (e) What is the vector f^? (Express your answer in vector form.) r^ = (f) What is the value of 14πε0 q|r→|2? N/C (g) Finally, what is the electric field, expressed as a vector? (Express your answer in vector form.) E→ = N/C
The electric field at location B has the value < 5000, −5000, 0 > N/C. What is the unit vector in the direction of E→ at this location? E^ = What is the electric force on the −8e−09 C charge? F→ = N What is the unit vector in the direction of this electric force? F^ =
What is the electric field at a location b→ = < −0.2, −0.5, 0 > m, due to a particle with charge +3 nC located at the origin? E→ = < > N/C
Figure shows a nonconducting rod of length L = 5.5 cm has a nonuniform charge density λ = −2x. (a) Find the Potential at point P which is at a distance a = 10 cm from the rod. 4 (b) The electric potential at points in an xyz plane is given by V = (5.0 V/m2) x2y + (4.0 V/m4) y3z + (6.0 V/m3) yz2. In unit-vector notation, what is the electric field at the point (3.0 m, −2.0 m, 9 m) and the magnitude of the field? 4