Physics Answers

7. Show that if the linear operators Aˆ and Bˆ do not commute, the operators

(AˆBˆ + BˆAˆ) and i[A, ˆ Bˆ] are Hermitian.

6. Show that xe−x

2

is an eigenfunction of the linear operator d

2

dx2 − 4x

2

.

What is the eigenvalue?

1)Two oppositely charged horizontal plates are separated by a distance d =1 cm and each has a length L =3 cm, see Fig. below. The electric field between the plates is uniform and has a magnitude E =102 N/m. An electron is projected between the plates with a horizontal initial speed of 𝑣0=106 𝑚/𝑠 as shown. Assuming this experiment is conducted in a vacuum, where will the electron strike the upper plate? Repeat when a proton replaces the electron.

1)Two-point charges q1=+9μC and q2=−4μC are separated by a distance L =10 cm, see Fig. below. Find the point at which the resultant electric field is zero.

2)Two identical small spheres of mass m and charge q hang from non-conducting strings, each of length L. At equilibrium, each string makes an angle θ with the vertical, see Fig. below (a) When θ is so small that tanθ ≈ sin θ, show that the separation distance r between the spheres is 𝑟=(𝐿𝑞2/2𝜋𝜖0𝑚𝑔)13. (b) If L =10 cm, m=2 g, and r =1.7 cm, what is the value of q?

1. Explain the working of a full-wave bridge rectifier with a neat circuit diagram and waveform.

1. Explain the construction and working of Strain gauge

1. Explain the construction and working of LVDT

An ion with a charge of +3.2 × 10–19 C and a mass of 2.7 × 10–26 kg is moving due south at a speed of 4.8 × 103 m s–1 . It enters a uniform magnetic !eld of strength 4.6 × 10–4 T directed downwards towards the ground. Determine the force acting on the ion. 

A straight wire of length 0.75 m carries a current of 35 A. The wire is at right angles to a magnetic field of strength 0.058 T. Calculate the force on the wire.

A battery is connected in series with a resistor R. The battery transfers 2000 C of charge completely round the circuit. During this process, 2500 J of energy is dissipated R and 1500 J is expended in the battery. Calculate the emf of the battery.