Write general expressions for the electric and magnetic fields of a 1 GHz sinusoidal plane wave traveling in the +y direction in a lossless nonmagnetic medium with relative permittivity ϵr=9. The electric field is polarized along the x direction, its peak value is 6 V/m, and its intensity is 4 V/m at t=0 and y=2 cm.

In a vernier instrument the main scale is in 1/2 mm divisions .vernier is made by redividing 19 such divisions into 20 equal parts. calculate the least count of the instrument.

Jason and mia are both running in a race. as they approach the finish line, you being the physicist that you are decide to time how long it takes them to reach the end of the race. when you start your stop watch (you can take this as time t = 0 s) you notice that mia is an unknown distance d ahead of jason and both are moving with the same initial velocity v_0. you also notice that jason is accelerating at a constant rate of a_j, while mia is deaccelerating at a constant rate of -a_m. jason and mia meet each other for the first time at time t = t_1. at this time (t = t_1) jason's velocity is two times that of mia's velocity, meaning v_j (t_1) = 2v_m (t_1). a) draw the position vs. time graph describing mia's and jason's motion from time t = 0 to time t = t_1. clearly label your axes and initial conditions on your graph. b) draw the velocity vs. time graph describing mia and jason's motion from time t = 0s to time t = t_1. clearly label your axes and initial conditions on your graph. c) how long from when the stop watch was started at t = 0s did it take mia and jason to meet? express your answer in terms of know quantities v_0, a_m, and a_j. d) when the stop watch started at time t = 0s, how far apart, d, were mia and jason? express your answer in terms of know quantities v_0, a_m, and a_j.

Avery long solenoid of inner radius 2.75 cm creates an oscillating magnetic field of the form = for this solenoid, =0.00425 t and =319 rad/s. (a)what is the maximum value of the induced electric field at a perpendicular distance 1.45 cm from the axis of the solenoid? (b) what is the maximum value of the inducted electric field at a point 5.85 cm perpendicular from the axis of the solenoid?