Forces and Motion
A charged particle is released at rest in a region where both a uniform electric field and a uniform magnetic field are present. The fields are perpendicular to each other, and the particle begins to spiral. What is the radius of the spiral after it achieves a steady velocity?
r = mv/qB (Radius of circular motion due to magnetic force)
A loop of radius R rotates with angular velocity ω in a uniform magnetic field, B. Find the emf induced in the loop as a function of time if the axis of rotation is along its diameter.
ε =−dΦB/dt
A point charge q is located at the center of a spherical shell of radius R. Calculate the potential at the surface of the shell.
V=ke(q/R)
A cylindrical rod with a non-uniform charge density ρ(r)=ρ0r2 (where ρ0 is a constant and r is the radial distance) is surrounded by a conducting shell. What is the electric field at a point inside the rod, inside the shell, and outside the shell?
Gauss’s Law, ΦE=∮E⋅dA=qenc/ϵ0
In the formula for capacitance of a parallel plate capacitor, what does the variable d represent?
d represents the distance between the plates of the capacitor.
You're an engineer designing a robotic arm with a current-carrying wire inside a rotating magnetic field. The wire is part of a circuit, and you need to calculate the magnetic force acting on it as the arm moves. The current in the wire, I=2.0, length of wire, L=0.5 mL, magnetic field strength, B=0.8, and the angle θ=30∘ at a specific position of the arm
F=ILBsinθ (Magnetic force on a current-carrying wire)
A coil with N turns is connected to a resistor R. The current through the coil is increasing linearly with time, such that I(t)=kt. What is the induced emf in the coil at time t, and how does it affect the voltage across the resistor?
εL=−L(dI/dt)
A long-charged rod with uniform charge distribution has linear charge density λ. Calculate the electric field at a point a distance r from the rod (assuming the rod extends infinitely in length).
E=2keλ/r
Consider a solenoid with a radius of 0.040 m and 120 turns, carrying a constant current of 0.50 A. What is the magnetic field at the center of the solenoid?
B=μ0nI
In the formula for mutual inductance M, what does the variable A stand for?
A represents the cross-sectional area of the solenoid
A square loop of side L carrying a current I is placed in a uniform magnetic field B such that its plane is at an angle θ to the field. What is the torque on the loop?
τ=IABsinθ
A capacitor in an RC circuit is initially uncharged. A switch is closed, and the capacitor charges over time by a battery with an emf = 100V. Calculate the current in the circuit at time t=τ.
I(t)=(ε/R)e−t/τ
Two parallel plate capacitors, one with a dielectric and the other without, are charged to the same potential difference and then disconnected from their power supplies. If the dielectric is slowly removed from the first capacitor, how does the energy stored in the entire system change?
U=1/2(CΔV)2 (energy stored in a capacitor)
A circular loop of radius R carrying a current I produces a magnetic field at its center. Find the magnitude of this field.
B=μ0NI/2R
In the formula for inductive reactance XL, what does the variable ω stand for?
ω represents the angular frequency of the AC source
A charged particle is moving in a circular path with radius r under the influence of a perpendicular uniform magnetic field B. The magnetic field is suddenly doubled. Determine the new angular velocity of the particle
ω=qB/m
What is inductance? What is an AC circuit?
The process of generating current in a conductor by placing it in a changing magnetic field is called induction.
An alternating current (AC) circuit is an electrical circuit that regularly reverses direction and changes its value constantly with time
You are tasked with designing a magnetic energy storage system. You have an inductor with a certain inductance L, connected to a power supply that provides a current I. The system is designed to charge the inductor and store energy in its magnetic field. If the current in the inductor reaches a maximum value of 3 A, how much energy is stored in the magnetic field of the inductor at that moment?
U=1/2 LI2
A solenoid with N1 turns and length L1 carries a time-varying current I1(t)=I0sin(ωt). A second solenoid with N2 turns is placed coaxially with the first. Calculate the induced emf in the second solenoid, given M.
ε2=-M dI1/dt
In the formula for the magnetic field inside a solenoid, what does the variable n represent?
n represents the number of turns per unit length of the solenoid
A proton moving with velocity V enters a magnetic field B at an angle θ. What is the time it takes to complete one helical cycle?
T=2πm/qB
A solenoid has N=100N, length L=0.5 mL, and cross-sectional area A=2×10−4 m2. The solenoid is connected to a circuit, and the current through it changes over time. How much will the solenoid oppose the current?
L=μ0N2AD
This equation describes a ratio that measures the efficiency of a system's ability to provide heating or cooling relative to the amount of energy it consumes
COPh = |Qh|/W
COPc = |Qc|/W
A current I flows through a long, straight wire bent into a semi-circular arc with radius R. The wire lies in the xy-plane, and the center of the semi-circle is at the origin. Calculate the magnetic field at a point on the z-axis, a distance z from the center of the semi-circle, due to the current.
B=μ0/4π∫(Idl×r)/r2
What is the difference between Supplemental Instruction and tutoring services and why are they different?
SI focuses on a collaborative group learning environment, where students actively discuss and review course material together to develop study strategies in various creative ways. Tutoring typically provides general academic support depending on the student's learning gaps and needs