E&M Fields
Potential and Force Dynamics
Circuits
Induction and Waves
100
The electron in a hydrogen atom orbits the proton at a radius of 0.053 nm. What is the electric field due to the proton at the position of the electron?
E=5.1\times10^11\text{N/m}
100
All the charges have the same magnitude. In which case does the electric field at the dot have the largest magnitude?
100
Draw a circuit diagram for the following image:
100
At a particular location the earth's magnetic field is 50\ \mu\text{T} tipped at an angle of 60^{\circ} below the horizontal. A 10 cm diameter circular loop of wire sits flat on a table. What is the magnetic flux through the loop?
\Phi_B=3.4\times10^{-7}\text{ Wb}
200
A typical MRI solenoid has a length of about 1m and a diameter of about 1m. A typical field inside such a solenoid is 1T. How many turns of wire must the solenoid have if the largest current the wire can carry is 100A?
N=8000 turns
200
Find the direction and magnitude of the electric force of the bottom charge:
1.1 \times 10^{-5}\ N, upwards.
200
Find the current and voltage of every resistor of the following diagram:
I_1 = 0.5\ A, \Delta V_1 = 6.0\ V
I_2 = 0.3\ A, \Delta V_2 = 6.0\ V
I_3 = 0.2\ A, \Delta V_3 = 6.0\ V
200
Ultraviolet radiation with a wavelength of 254 nm is used in germicidal lamp. What is the photon energy in eV for such a lamp?
E=4.89\text{ eV}
300
A dipole consists of a +1.5\text{ nC and }-1.5\text{ nC} charge separated by 1.2 cm, with the positive charge on the right. What is the electric field strength at the point 1.2 cm to the right of the positive charge?
7.0\times10^{4}\text{ N/C}
300
This parallel plate capacitor is charged to 5000\ V. A proton is fired into it with an initial speed of 3.0 \times 10^5\ \text{m/s}. Find the impact speed of the proton on the plate.
7.5 \times 10^5\ \text{m/s}
300
Assume that the switch has been in the shown position for a long time, meaning that the capacitor is fully charged. Let the switch change its position at t = 0\ \text{s}.
a) What is the current in the circuit the moment it's switched?
b) What is the current in the circuit 25\ \mu\text{s} later?
a)
I_0 = 0.9\ \text{A}
b)
I = 0.074\ \text{A}
300
A wire of resistance R is sliding on a U shaped conducting rail. Assuming that the rail is an ideal wire, what will the current in the wire be?
I=\frac{\epsilon}{R}=\frac{vlB}{R}
400
Two long, straight wires lie in parallel to each other, as shown in the figure. They each carry a current of 5.0 A, but in different directions. What is the magnetic field at point P?
\vec{B}=6.3\ \mu\text{T} into the page
400
Three charged particles with q_1=-50\text{ nC},q_2=+50\text{ nC, and }q_3=+30\text{ nC} are placed as shown. What is the net charge on q_3 due to the other charges?
\vec{F}_3=-3.8\times10^{-3}\text{ N}\hat{x}
400
Consider an AC circuit with a 60 Hz AC signal of 15 V, in which a 40 µF capacitor is in series with a 30 Ω resistor and a 100 mH inductor.
What are the capacitive reactance and the inductive reactance of the circuit?
X_C = 66.3\ \Omega
X_L = 37.7\ \Omega
400
A cell phone emits 0.6 W of 1.9 GHz radio waves. What are the amplitudes of the electric and magnetic fields at a distance of 10 cm?
E_0=60\text{ V/m}
B_0=2.0\times10^{-7}\text{ T}
500
Green turtles are thought to navigate by using the dip angle of the earth's magnetic field. To test this hypothesis, green turtle hatchlings were placed inaa a 72-cm diameter tank with a 60-turn coil of wire wrapped around the outside. A current in the coil created a magnetic field at the center of the tank that exactly canceled the vertical component of the earth's 50\ \mu\text{T} field. At the location of the test, the earth's field was directed 60^{\circ} below the horizontal. What was the current in the coil?
I=0.41\text{ A}
500
It takes a proton with a kinetic energy of 11 MeV to efficiently change O nuclei into F nuclei. If the magnetic field inside a cyclotron is 1.2 T, what is the radius of the protons orbit right before they exit the cyclotron.
r=0.4\text{ m}
500
An AM radio antenna picks up a 1000 kHz signal with a peak voltage of 5.0 mV. The tuning circuit consists of a 60\ \mu\text{H} inductor in series with a variable capacitor. The inductor coil has a resistance of 0.25\Omega , and the resistance of the rest of the circuit is negligible.
a) To what value should the capacitor be tuned to listen to this radio station?
b) What is the peak current through the circuit at resonance?
c) A stronger station at 1050 kHz produces a 10 mV antenna signal. What is the current at this frequency when the radio is tuned to 1000 MHz?
a)
C=420\text{ pF}
b)
I_{max}=20\text{ mA}
c)
I=0.26\text{ mA}
500
A 20 cm long, zero resistance wire is pulled outwards on zero resistance rails at a steady speed of 10 m/s in a 0.1T magnetic field. On the opposite side a 0.1\Omega resistor completes the circuit by connecting to the two rails.
How much force is required to pull the wire at this speed?
F=4\text{ mN}