A planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).

What are the expected readings of the ammeter and voltmeter for the circuit in the figure below? (R = 5.60 Ω, ΔV = 6.30 V) ammeter     I =

simple diagram to illustrate the setup for each law- coulombs law and biot savart law

A circular coil with 100 turns and a radius of 0.05 m is placed in a magnetic field that changes at auniform rate from 0.2 T to 0.8 T in 0.1 seconds. The plane of the coil is perpendicular to the field.• Calculate the induced electric field in the coil.• Calculate the current density in the coil given its conductivity σ.

An L-C circuit has an inductance of 0.410 H and a capacitance of 0.250 nF . During the current oscillations, the maximum current in the inductor is 1.80 A . What is the maximum energy Emax stored in the capacitor at any time during the current oscillations? How many times per second does the capacitor contain the amount of energy found in part A? Please show all steps.

A long, straight wire carries a current of 10 A along what we’ll define to the be x-axis. A square loopin the x-y plane with side length 0.1 m is placed near the wire such that its closest side is parallel tothe wire and 0.05 m away.• Calculate the magnetic flux through the loop using Ampere’s law.

Describe the motion of a charged particle entering a uniform magnetic field at an angle to the fieldlines. Include a diagram showing the velocity vector, magnetic field lines, and the path of the particle.

Discuss the differences between the Biot-Savart law and Coulomb’s law in terms of their applicationsand the physical quantities they describe.

Explain why Ampere’s law can be used to find the magnetic field inside a solenoid but not outside.