Two long, straight parallel wires are laid on the ground and aligned in the East-west direction. The current in the northern wire is 8.00 A and is heading to the east. The current in the southern wire is 6.00 A and is heading west. They are separated by 0.0230 m. What is the magnitude of the magnetic field 0.0100 m south of the northern most wire?
A hollow cylindrical conductor of inner radius 0.0143 m and outer radius 0.0274 m carries a uniform current of 5.16 A. What is the current enclosed by an Amperian loop of radius 0.0174 m?
The figure below shows the cross section of three long straight current carrying wires. Wire a carries a current of 8.22 A, wire b carries a current of 6.95 A, and wire c carries a current of 1.98 A. What is the magnitude of ∮ B⃗ ⋅ ds for a clockwise Amperian loop that surrounds all three wires?
The figure provided shows the tracks from a bubble chamber experiment. If all of the particles shown have the same-speed and the same mass, which particle has the greatest amount of charge? particle A particle E particle C particle D particle B
The strength of the magnetic field at the center of two concentric current loops is zero. The smaller loop has a radius of 0.0390 m and a current of 13.0 A. The larger current loop has a radius of of 0.108 m. What is the current through the larger loop?
A wire is bent into a 5.60 cm radius circular loop. What current is needed to cancel the Earth's magnetic field (50.0 μT) at the center of the loop? A
A current carrying wire can produce a magnetic field no stronger than 4.0 × 10-5 T at a distance of 5 cm away from its center. What is the largest current it can carry? 10.0 A 30.0 A 5.0 A 20.0 A
The figure below shows the cross section of a long cylindrical conducting cylinder of radius a = 0.0824 m. The current density in the cross section is given by J = (6.44 × 106 A/m3) r. Where inside the cylinder does the magnetic field have a magnitude of 1.14 × 10-3 T?
The figure provided shows the tracks from a bubble chamber experiment. Which of the particles has no charge? particle A particle E particle C particle D particle B
An electron is moving in the xz plane, and at a particular instant the electron has the velocity vector components vx = -5.0 × 105 m/s and vz = 3.0 × 105 m/s. The electron is moving through a region of uniform magnetic field with magnitude 0.80 T oriented in the positive x direction. What is the magnetic force experienced by the electron, in newtons, at the instant in question? 7.5 × 10-14 N in the negative y direction 6.4 × 10-14 N in the positive y direction 3.8 × 10-14 N in the positive y direction 6.4 × 10-14 N in the negative y direction 3.8 × 10-14 N in the negative y direction
A proton is moving in the xz plane, and at a particular instant, the proton has the velocity vector components vx = -5.0 × 105 m/s and vz = 3.0 × 105 m/s. The proton is moving through a region of uniform magnetic field with magnitude 0.80 T oriented in the positive x direction. What is the magnetic force experienced by the proton, in newtons, at the instant in question? 6.4 × 10-14 N in the positive y direction 7.5 × 10-14 N in the positive y direction 3.8 × 10-14 N in the negative y direction 3.8 × 10-14 N in the positive y direction 7.5 × 10-14 N in the negative y direction
A proton is moving in the xy plane, and at a particular instant, the proton has the velocity vector components vx = 5.0 × 105 m/s and vy = 3.0 × 105 m/s. The proton is moving through a region of uniform magnetic field with magnitude 0.80 T oriented in the positive x direction. What is the magnetic force experienced by the proton, in newtons, at the instant in question?
A proton moves through a uniform magnetic field. The magnetic field is given by B⃗ = (0.00iˆ - 29.4jˆ + 47.4kˆ )mT. At a moment in time when the velocity is v = (0.00iˆ + vyjˆ + 69600.00kˆ) m/s, the magnetic force acting on the proton is F = (5.42iˆ + 0.00jˆ + 0.00 kˆ) × 10-16 N. What is the value of vy?
An electron moves through a uniform magnetic field. The magnetic field is given by B⃗⃗ = (0.00iˆ - 42.0jˆ + 62.0kˆ )mT. At a moment in time when the velocity is v = (0.00iˆ + vyĵ+ 87300.00kˆ) m/s, the magnetic force acting on the electron is F = (5.09iˆ + 0.00jˆ + 0.00kˆ) × 10-16 N. What is the value of vy? m/s
A proton (charge e), traveling perpendicular to a magnetic field, experiences the same force as an alpha particle (charge 2e ) which is also traveling perpendicular to the same field. The ratio of their speeds, vproton/valpha is 1 2 0.5 4 8
An electron (charge = -1.6 × 10-19C ) is moving at 3.0 × 105 m/s in the positive x direction. The electron enters a magnetic field of 0.80 T in the positive z direction. The magnetic force on the electron is 3.8 × 10-14 N in the negative y direction. 0 N. 3.8 × 10-14 N in the positive z direction. 3.8 × 10-14 N in the negative z direction. 3.8 × 10-14 N in the positive y direction.
Figure (a) shows an element of length ds = 1.24 μm in a very long straight wire carrying current. The current in that element sets up a differential magnetic field dB at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 5.6 cm from the element, as a function of angle θ between the wire and a straight line to the point. The vertical scale is set by dBs = 60.2 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 5.6 cm from the wire? Number Units
A straight conductor carrying a current i = 7.8 A splits into identical semicircular arcs as shown in the figure. What is the magnetic field at the center C of the resulting circular loop, which has a radius of 6.2 cm?
In the figure, two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius 1.50 cm and carries 4.20 mA. Loop 2 has radius 2.20 cm and carries 6.30 mA. Loop 2 is to be rotated about a diameter while the net magnetic field B⃗ set up by the two loops at their common center is measured. Through what angle must loop 2 be rotated so that the magnitude of the net field is 102 nT? Number Units
A current is set up in a wire loop consisting of a semicircle of radius 4.31 cm, a smaller concentric semicircle, and two radial straight lengths, all in the same plane. Figure (a) shows the arrangement but is not drawn to scale. The magnitude of the magnetic field produced at the center of curvature is 47.42 μT. The smaller semicircle is then flipped over (rotated) until the loop is again entirely in the same plane (Figure (b)). The magnetic field produced at the (same) center of curvature now has magnitude 16.08μT, and its direction is reversed. What is the radius of the smaller semicircle? Number Units
In Figure (a), wire 1 consists of a circular arc and two radial lengths; it carries current i1 = 0.700 A in the direction indicated. Wire 2, shown in cross section, is long, straight, and perpendicular to the plane of the figure. Its distance from the center of the arc is equal to the radius R of the arc, and it carries a current i2 that can be varied. The two currents set up a net magnetic field B⃗ at the center of the arc. Figure (b) gives the square of the field's magnitude B 2 plotted versus the square of the current i2 2 . The vertical scale is set by Bs 2 = 10.9 × 10-10 T 2 . What angle is subtended by the arc? Number Units
A particle undergoes uniform circular motion of radius 14.5 μm in a uniform magnetic field. The magnetic force on the particle has a magnitude of 2.40 × 10-17 N. What is the kinetic energy of the particle? Number Units
A source injects an electron of speed v = 2.7 × 107 m/s into a uniform magnetic field of magnitude B = 2.7 × 10-3 T. The velocity of the electron makes an angle θ = 8.9∘ with the direction of the magnetic field. Find the distance d from the point of injection at which the electron next crosses the field line that passes through the injection point. Number Units
In a certain cyclotron a proton moves in a circle of radius 0.540 m. The magnitude of the magnetic field is 1.60 T. (a) What is the oscillator frequency? (b) What is the kinetic energy of the proton? (a) Number Units (b) Number Units
In the figure, a long straight wire carries a current i1 = 32.3 A and a rectangular loop carries current i2 = 25.7 A. Take a = 1.40 cm, b = 10.4 cm, and L = 44.9 cm. What is the magnitude of the net force on the loop due to i1? Number Units
A circular loop of radius 7.3 cm carries a current of 17 A. A flat coil of radius 1.0 cm, having 70 turns and a current of 1.3 A, is concentric with the loop. The plane of the loop is perpendicular to the plane of the coil. Assume the loop's magnetic field is uniform across the coil. What is the magnitude of (a) the magnetic field produced by the loop at its center and (b) the torque on the coil due to the loop? (a) Number Units (b) Number Units
Three long wires all lie in an xy plane parallel to the x axis. They intersect the y axis at the origin, y = d, and y = 2d, where d = 13 cm. The two outer wires each carry a current of 6.4 A in the positive x direction. What is the magnitude of the force on a 4.9 m section of either of the outer wires if the current in the center wire is 3.5 A (a) in the positive x direction and (b) in the negative x direction? (a) Number Units (b) Number Units
An RLC series circuit is connected to an oscillator with a maximum emf of 100 V. If the voltage amplitudes VR, VL, and VC are all equal to each other, then VR must be 67 V. 87 V. 100 V. 33 V. 50 V.
Which of the following combinations of units is equivalent to a Volt? A m2 T B m2Ts-1 C mTs-1 D Ts-1
Which of the following is equivalent to the units of inductance in base SI units? kg ⋅ m /s ⋅ A2 kg ⋅ m2/s2 A kg2 m/s 2 A2 kg ⋅ m2/s 2 A2
Faraday’s law states that the EMF around a closed loop is equal to which of the following quantities? The flux of the electric field through a surface which has the loop as its boundary. The negative of the time rate of change of the flux of the magnetic field through a surface which has the loop as its boundary. The line integral of the magnetic field around the closed loop. The flux of the magnetic field through a surface which has the loop as its boundary.
In an oscillating LC circuit, the total stored energy is U and the maximum current in the inductor is I. When the current in the inductor is 1/2, the energy stored in the capacitor is 3U/4. 4U/3. 3U/2. U/4. U/2.
A solenoid with an self-inductance L carries a current described by i(t) = bt. Which of the given equations describes the EMF induced in the coil? ε = -L/b ε = -Lbt ε = - Lbt^2/2 ε = -Lb
At time t = 0, the charge on the 50 - μF capacitor in an LC circuit is 15 μC, and there is no current. If the inductance is 20 mH, the maximum current is 15 mA. 15 A. 15 nA. 6.7 mA. 15 μA.
In an RLC series circuit, which is connected to a source of emf Emcos(ωt), the current lags the voltage by 45∘ if R = 1/ωL - ωC ωL = 1/ωC R = 1/ωC - ωL R = ωC – 1/ωL R = ωL – 1/ωC
The figure below shows a loop of wire of radius r = 0.810 m and resistance R = 0.0210Ω inside a region of spatially constant magnetic field with time dependent magnitude B = bt Find the time at which the net magnetic field at the center of the loop vanishes.
A rectangular toroid and a cylindrical solenoid have equal cross-sectional areas, equal inductances, the same number of total turns, and the length of the solenoid is the same as the average circumference of the toroid. What is the ratio of the outer radius to the inner radius of the toroid? Hint: the inductance of a rectangular toroid with outer and inner radii R1 and R2, respectively, with N number of turns and a height h is L = μ0N2h/2π ln (R2/R1). R2/R1 = e The described situation is impossible to achieve with an actual solenoid and toroid. R2/R1 = 3 R2/R1 = 2
An LC circuit has an inductance of 20.0mH and a capacitance of 5.0 μF. If the charge amplitude is 40.0 μC, what is the current amplitude? 7.9 A 1.0 A 0.025 A 0.13 A 400 A
A circular loop of wire of radius r = 0.124 m and resistance R = 3.44 Ω lies in a plane perpendicular to a spatially constant magnetic field of initial magnitude B(0) = 5.49 T. If the field is reduced to zero, what is the magnitude of the total charge that moves through the loop. This value of charge is independent of the function B(t) that takes the field to zero.
An ac generator producing an emf with an amplitude of 10.0 V at 250.0 rad/s is connected in series with a 60.0 - Ω resistor, a 30.0-mH inductor, and a 90.0 - μF capacitor. The current amplitude is 0.167 A 0.139 A 0.212 A 0.142 A 1.41 A.
An RC series circuit is connected to an emf source having angular frequency ω. The current lags the source emf by tan-1 (1/ωCR). leads the source emf by tan-1 (1/ωCR). leads the source emf by π/4. leads the source emf by tan-1 (ωCR). lags the source emf by tan-1 (ωCR).
A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is: BAf/2π BAf 2BAf 2πBAf 4πBAf
A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at: 0 rad/s 2.7 rad/s 5.6 rad/s 35 rad/s 71 rad/s
A rod of length L and electrical resistance R moves through a constant uniform magnetic field B; both the magnetic field and the direction of motion are parallel to the rod. The force that must be applied by a person to keep the rod moving with constant velocity v is: 0 BLV BLv/R B2L2v/R B2L2v2/R
As a loop of wire with a resistance of 10 Ω moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop is: 0 V 0.22 V 0.28 V 2.0 V cannot be calculated from the given data
A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them. When the total emf of the combination is 16 V, the emf of the larger inductor is: 2.3 V 7.0 V 9.0 V 28 V 36 V
A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is: 2.0 × 103 A/s 3.6 × 103 A/s 4.6 × 103 A/s 7.0 × 103 A/s 8.1 × 103 A/s
An inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf E. A switch in the circuit is closed at time t = 0, at which time the current is zero. A long time after the switch is thrown the potential differences across the inductor and resistor are: 0, E E, 0 E/2, E/2 (L/R)E, (R/L)E unknown since the rate of change of the current is not given
An LC circuit has an inductance of 15 mH and a capacitance of 10 µF. At one instant the charge on the capacitor is 25 µC. At that instant the current is changing at the rate: 0 A/s 1.7 × 10-7 A/s 5.9 × 10-3 A/s 3.8 × 10-2 A/s 170 A/s
A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the initial charge on the capacitor is: 0.15 C 0.25 C 8.8 C 15 C 35 C
Radio receivers are usually tuned by adjusting the capacitor of an LC circuit. If C = C1 for a frequency of 600 kHz, then for a frequency of 1200 kHz one must adjust C to: C1/2 C1/4 2C1 4C1 √2C1
A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant what is the potential difference across the capacitor? 0 V 5 V 10 V 15 V 20 V
The total energy in an LC circuit is 5.0 × 10-6 J. If L = 25 mH the maximum current is: 10 mA 14 mA 20 mA 28 mA 40 mA
An LC circuit has a capacitance of 30 µF and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 µC and the current is 20 mA. The maximum charge on the capacitor is: 8.9 µC 10 µC 12 µC 17 µC 24 µC
An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50 - Ω resistor, a 400 - mH inductor, and a 200 - µF capacitor. The rms voltage across the inductor is: 2.5 V 3.4 V 6.7 V 10.0 V 10.8 V
An electric generator contains a coil of 150 turns of wire, each forming a rectangular loop 67.7 cm by 24.9 cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 3.21 T and initially perpendicular to the coil's plane. What is in volts the maximum value of the emf produced when the loop is spun at 970 rev/min about an axis perpendicular to the magnetic field? Number Units
The current i through a 3.6 H inductor varies with time t as shown by the graph of the figure. The inductor has a resistance of 12 Ω. Find the magnitude of the induced emf ε during the time intervals (a) t = 0 to 2 ms; (b) 2 ms to 5 ms, and (c) 5 ms to 6 ms. (Ignore the behavior at the ends of the intervals.) (a) Number Units (b) Number Units (c) Number Units
A series RLC circuit has a resonant frequency of 5.28 kHz. When it is driven at 8.29 kHz, it has an impedance of 1.15 kΩ and a phase constant of 53.0∘. What are (a) R, (b) L, and (c) C for this circuit? (a) Number Units (b) Number Units (c) Number Units
If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be: twice the old four times the old half the old one-fourth the old unchanged
The current in an RL circuit builds up to 30.0% of its steady-state value in 7.00 s. What is the inductive time constant (s) ? 29.8 22.7 33.3 15.4 5.67 19.6 8.99 66.7 43.1 91.2
A long solenoid of radius 2.50 cm has 3000 turns of wire per meter. The current in the solenoid increases at a rate of 0.150 A/s. What is the magnitude of the induced electric field (V/m) 3.50 cm from the axis of the solenoid? 3.22 × 10-6 7.07 × 10-6 5.05 × 10-6 2.80 × 10-6 4.36 × 10-6 1.61 × 10-6 2.01 × 10-6 9.90 × 10-6 8.56 × 10-6 6.39 × 10-6