Given a magnetic field with cylindrical symmetry B=B(r)k with r the distance yo the symmetry axis....
Given
a magnetic field with cylindrical symmetry B=B(r)k with r
the distance yo the symmetry axis. An ion with charge q and mass m
moves un a circular orbit of radius R from the symmetry axis with
angular velocity ω=B(r) (q/m).
If the magnetic field is slowly increased in magnitude, show that
the emf that is induced on the ion's orbit is such that the ion
accelerates. Show that for the ion to remain in the same orbit, the
average increase in B(r) on the surface enclosed by the orbit must
be double the change un B(r)
Homework Answers
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Given
a magnetic field with cylindrical symmetry B=B(r)k with r
the distance yo the symmetry axis....
A cylindrical shell with radius R and length W carries a uniform chargeQ and rotates about its axis with angular speed ω.
A cylindrical shell with radius R and
length W carries a uniform chargeQ and rotates about its axis with angular
speed ω. The center of the cylinder lies
at the origin O and its axis is
coincident with the x-axis, as shown in
(Figure 1).Part AWhat is the charge density σ?Express your answer in terms of the variables Q, R, and W.σ =______________Part BWhat is the differential current dI on
a circular strip of the cylinder centered at x and with width dx?Express your...
The induced magnetic field at a radial distance r from the central axis of a circular...
The induced magnetic field at a radial distance r from the central axis of a circular parallel-plate capacitor is B. If the capacitor plates have a radius R, write an expression for the rate dE/dt at which the electric field between the plates is changing.
Problem 3 Part A A copper wire with resistance 0.010 Ω is shaped into a complete circle of radius R 10 cm and placed in a long solenoid so that the axis of the solenoid and the axis of the wire loop...
Problem 3 Part A A copper wire with resistance 0.010 Ω is shaped into a complete circle of radius R 10 cm and placed in a long solenoid so that the axis of the solenoid and the axis of the wire loop coincide. The current in the solenoid is turned on and then slowly decreased. The magnetic field strength is initially B 0.750 T and subsequently decreases in time at the constant rate -0.035 T/s. (a) Calculate the induced emf...
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A generator is constructed by rotating a coil of N turns in a magnetic field B...
A generator is constructed by rotating a coil of N turns in a magnetic field B at a frequency f. The internal resistance of the coil is R and the cross sectional area of the coil is A. Which of the following statements are true? (Give ALL correct answers, i.e., B, AC, BCD...) A) The maximum induced EMF doubles if the frequency f is doubled. B) The maximum induced EMF doubles if the magnetic field B is doubled. C) The...
A generator is constructed by rotating a coil of N turns in a magnetic field B...
A generator is constructed by rotating a coil of N turns in a magnetic field B at a frequency f. The internal resistance of the coil is R and the cross sectional area of the coil is A. The average induced EMF doubles if the magnetic field B is doubled. The average induced EMF doubles if the area A is doubled. The average induced EMF doubles if the frequency f is doubled. The average induced EMF doubles if the resistance...
A circular loop (r = 0.10m) is placed in a uniform magnetic field of magnitude B...
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4.) For the slidewire generator below, the magnetic field is a constant 2.0 T into the...
4.) For the slidewire generator below, the magnetic field is a constant 2.0 T into the page, the length L is 0.50 m and the conducting slidewire moves at 5.5 m/s. The total resistance of the circuit is R=1.5 Ω. a.) Find the induced current (7 pts). b.) How much power is dissipated? (6 pts) c.) In what direction does the induced current flow? (3 pts) A current carrying circular loop with N-50 turns rotates in a 2.0 T magnetic...
A circular loop is placed in air (E-H) to measure the electromagnetic field from a test system at...
Please show all work clearly, thank you!
A circular loop is placed in air (E-H) to measure the electromagnetic field from a test system at (20%)2. frequency 5xx10's, see figure below. The region is source free, and the loop lies on the xy plane and has a radius a-0.5 m and resistance R-0.1 Ω. Due to an induced emf, a current flows in the loop and is measured to be 20 mA (peak magnitude is 20 mA). The E-field is...
A generator is constructed by rotating a coil of N turns in a magnetic field B...
A generator is constructed by rotating a coil of N turns in a magnetic field B at a frequency f. The internal resistance of the coil is R and the cross sectional area of the coil is A. True or False 1. The average induced EMF doubles if the resistance R is doubled 2. The average induced EMF doubles if the magnetic field B is doubled 3. The maximum induced EMF occurs when the coil is rotated about an axis...
A cylindrical shell with radius R and
length W carries a uniform chargeQ and rotates about its axis with angular
speed ω. The center of the cylinder lies
at the origin O and its axis is
coincident with the x-axis, as shown in
(Figure 1).Part AWhat is the charge density σ?Express your answer in terms of the variables Q, R, and W.σ =______________Part BWhat is the differential current dI on
a circular strip of the cylinder centered at x and with width dx?Express your...
Problem 3 Part A A copper wire with resistance 0.010 Ω is shaped into a complete circle of radius R 10 cm and placed in a long solenoid so that the axis of the solenoid and the axis of the wire loop coincide. The current in the solenoid is turned on and then slowly decreased. The magnetic field strength is initially B 0.750 T and subsequently decreases in time at the constant rate -0.035 T/s. (a) Calculate the induced emf...
A circular loop of radius R is rotating with angular speed w to about Z-axis in a time-independent magnetic field, given by B = B_0 (cosa i + sina j). At t = 0, the loop lies in the Y-Z plane. Determine the magnetic flux psi and the induced EMF due to the magnetic field across the loop as a function of time.
A circular loop (r = 0.10m) is placed in a uniform magnetic field of magnitude B = 2.0T, where the face of the loop is perpendicular to the direction of the magnetic field a) What is the flux through the loop. b) the loop is rotated 90 degree in 30. What is the final flux? c) What is the induced emf during rotation?
4.) For the slidewire generator below, the magnetic field is a constant 2.0 T into the page, the length L is 0.50 m and the conducting slidewire moves at 5.5 m/s. The total resistance of the circuit is R=1.5 Ω. a.) Find the induced current (7 pts). b.) How much power is dissipated? (6 pts) c.) In what direction does the induced current flow? (3 pts) A current carrying circular loop with N-50 turns rotates in a 2.0 T magnetic...
Please show all work clearly, thank you!
A circular loop is placed in air (E-H) to measure the electromagnetic field from a test system at (20%)2. frequency 5xx10's, see figure below. The region is source free, and the loop lies on the xy plane and has a radius a-0.5 m and resistance R-0.1 Ω. Due to an induced emf, a current flows in the loop and is measured to be 20 mA (peak magnitude is 20 mA). The E-field is...
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