A 12.4 g wire of length 47.0 cm is suspended by a pair of flexible leads in a uniform magnetic field of magnitude 0.653T (see the figure). What is the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads? (a) Number Units (b)
In the figure, a particle moves along a circle in a region of uniform magnetic field of magnitude B = 3.2 mT. The particle is either a proton or an electron (you must decide which). It experiences a magnetic force of magnitude 3.1×10−15 N. What are (a) the particle's speed, (b) the radius of the circle, and (c) the period of the motion? (a) Number Units (b) Number Units (c) Number Units
In the figure, a parallel-plate capacitor has square plates of edge length L = 1.8 m. A current of 1.9 A charges the capacitor, producing a uniform electric field E→ between the plates, with E→ perpendicular to the plates. (a) What is the displacement current id through the region between the plates? (b) What is dE/dt in this region? (c) What is the displacement current encircled by the square dashed path of edge length d = 0.40 m? (d) What is ∮B→⋅ds→ around this square dashed path? Edge view Top view
Concept Simulation 11.1 reviews the concept that plays the central role in this problem. (a) The volume flow rate in an artery supplying the brain is 4.3×10−6 m3 /s. If the radius of the artery is 4.2 mm, determine the average blood speed. (b) Find the average blood speed as a constriction in the artery if the constriction reduces the radius by a factor of 2. Assume that the volume flow rate is the same as that in part (a). (a) Number Units (b) Number Units
A silver wire has resistivity ρ = 1.65×10−8 Ω⋅m and a cross-sectional area of 7.00 mmm2. The current in the wire is uniform and changing at the rate of 2700 A/s when the current is 160 A. (a) What is the magnitude of the (uniform) electric field in the wire when the current in the wire is 160 A? (b) What is the displacement current in the wire at that time? (c) What is the ratio of the magnitude of the magnetic field due to the displacement current to that due to the current at a distance r from the wire? (a) Number Units (b) Number Units (c) Number Units
An electron that has a velocity with x component 1.6×106 m/s and y component 3.9×106 m/s moves through a uniform magnetic field with x component 0.028 T and y component -0.18 T. (a) Find the magnitude of the magnetic force on the electron. (b) Repeat your calculation for a proton having the same velocity. (a) Number Units (b) Number Units
In the figure, a solid cylinder of radius 23 cm and mass 19 kg starts from rest and rolls without slipping a distance L = 4.5 m down a roof that is inclined at angle θ = 22∘. (a) What is the angular speed of the cyllinder about its center as it leaves the roof? (b) The roof's edge is at height H = 3.8 m. How far horizontally from the roof's edge does the cylinder hit the level ground? (a) Number Units (b) Number Units
The figure below shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 71.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. (1) (a) Calculate the speed of a link of the chain relative to the bicycle frame. (b) Calculate the angular speed of the bicycle wheels. (c) Calculate the speed of the bicycle relative to the road.
In the figure, an electron accelerated from rest through potential difference V1 = 1.07 kV enters the gap between two parallel plates having separation d = 19.5 mm and potential difference V2 = 177 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?
The figure shows a pendulum of length L = 2.0 m. Its bob (which effectively has all the mass) has speed v0 when the cord makes an angle θ0 = 31∘ with the vertical. (a) What is the speed of the bob when it is in its lowest position if v0 = 7.1 m/s? What is the least value that v0 can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if θ0 is increased by a few degrees?
In the figure, an electron accelerated from rest through potential difference V1 = 0.807 kV enters the gap between two parallel plates having separation d = 23.7 mm and potential difference V2 = 171 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap?
You are to throw a ball with a speed of 11.4 m/s at a target that is height h = 5.60 m above the level at which you release the ball (see the figure). You want the ball's velocity to be horizontal at the instant it reaches the target. (a) At what angle θ above the horizontal must you throw the ball? (b) What is the horizontal distance from the release point to the target? (c) What is the speed of the ball just as it reaches the target? (a) Number Units (b) Number Units (c) Number Units
A transformer has 660 primary turns and 13 secondary turns. (a) If Vp is 120 V (rms), what is Vs with an open circuit? If the secondary now has a resistive load of 12 Ω, what is the current in the (b) primary and (c) secondary? (a) Number Units (b) Number Units (c) Number Units
A 3.0 kg toy car can move along an x axis. The figure gives Fx of the force acting on the car, which begins at rest at time t = 0. The scale on the Fx axis is set by FXs = 4.0 N. In unit-vector notation, what is P→ at (a)t = 2.0 s and (b)t = 8.0 s, (c) what is v→ at t = 8.0 s? Fx(N) (a) Number i^ i j^ k^ Units (b) Number i^ + j^ + k^ Units (c) Number i^ + j^ + k^ Units
A ball is shot vertically upward from the surface of another planet. A plot of y versus t for the ball is shown in the figure, where y is the height of the ball above its starting point and t = 0 at the instant the ball is shot. The figure's vertical scaling is set by ys = 42.0 m. What are the magnitudes of (a) the free-fall acceleration on the planet and (b) the initial velocity of the ball?
Light traveling in a medium with a refractive index 1.44 is incident on a plate of another medium with index of refraction 1.98. At what angle of incidence is the reflected light fully polarized? Number Units
Suppose a 7.3×1010 kg meteoroid struck the earth at the equator with a speed v = 1.9×104 m/s, as shown in Fig. 11-27 and remained stuck (near the surface). What is the change in the length of the day (in seconds)? For moments of inertia of some common geometries, click here. If needed, the mass of the Earth is 5.97×1024 kg and the radius of the Earth is 6.38×106 m. Note that Desmos may be do a better job than your calculators of calculating the difference of two numbers which are very close to each other. s Figure 11-27