Do electrons tend to go to regions of high potential or low potential?

1

(a)

As electrons are negatively charged, they have tendency to go to regions of high potential.

Two charges of -9C and +9C are palced at the points P(1, 0, 4) and Q(2,-1, 5) located in an electric field E = 0.20i V/cm. Calculate the torque acting on the dipole.

1

(a)

As, P(1, 0,4) and (2,-1, 5)
\(\therefore \ 2l=PQ=[(2-1)\hat { i } +(-1-0)\hat { j } +(5-4)\hat { k] } \)
\(=(\hat { i } -\hat { j } +\hat { k } )\)
\(and \ q=\pm 9\times { 10 }^{ -6 }C,E=0.20\hat { i } V/cm.\tau =?\)
\(Since,\tau =\rho \times E=q(2l)\times E\)
\(\therefore \ \tau =9\times { 10 }^{ -6 }(\hat { i } -\hat { j } +\hat { k } )\times 0.20=18\times { 10 }^{ -7 }(\hat { k } -\hat { j) } \)
\(Magnitude\ of\ torque,\)
\(\tau =18\times { 10 }^{ -7 }[\sqrt { { (1) }^{ 2 }+{ (1) }^{ 2 } } ]=25.45\times { 10 }^{ -7 }N-m\)

Charge of 2C is placed at the centre of a cube volume 8 cm³. What is the electric flux passiing through one face?

1

(a)

Toral \(\phi \) = q0/\({ \varepsilon }_{ 0 }=2/{ \varepsilon }_{ 0 }\), \(\rightarrow\) flux through one face  = \(\phi \)/6 = 1/3 \({ \varepsilon }_{ 0 }\)

You are given 8 \(\Omega \) resistor. What length of wire of resistance 120 Ωm-1 should be joined in parallel with it to get a value of 6 \(\Omega \) ?

1

(a)

Now, 1/R=1R₁+1R₂
Because 1 = 48/240 = 0.2 m

What will be the direction of magnetic field at point O

1

(a)

The magnetic Field due to AB and EF is as the direction of length vector is along the radius vectorAlso the magnetic field due to BCE and BDE are equal opposite and equal so they cancel the effect of each other. So the net magnetic field at O is 0.

A bar magnet is cut into two pieces, along its length. How will its pole strength be affected?

1

(a)

M1 = M/2, M = M2

A current carrying solenoid of 100 turns has an area of cross section 10^-4 m² .When suspended freely through its centre, it can turn in a horizontal plane .what is the magnetic moment of the solenoid for a current of 5A.Also calculate the net force and torque on solenoid if a uniform horizontal field of 10x10^-2 T is set up at an angle of 30 degree with axis of solenoid when it is carrying the same current

1

(a)

M = nIA = 100 x 5 x 10^-4 = 500 x 10^-4 J/T
Net force = 0
Torque = MB sin \(\theta\) = 5 x 10² x 0.1 x sin30  = 25 x 10^-4 Nm
H = R cos \(\eth \) = 4 x 1/2 = 0.2 G

Define self-inductance in terms of work done against the induced emf.

1

(a)

Self - inductance is defined as double the work done against the induced emf in producing unit current in the coil itself \(L=\frac { 2W }{ { I }^{ 2 } } \)

Three students X, Y, and Z performed an experiment for studying the variation of alternating current with angular frequency in a series LCR circuit and obtained the graphs as shown. They all used a.c sources of the same r.m.s. value and inductances of the same value. What can we (qualitatively) conclude about the
(i) capacitance value
(ii) resistance values Used by them? In which case will the quality factor be maximum? What can we conclude about nature of the impedance of the setup at frequency w_o?

1

(a)

(i) Decreases From X to Z 
(ii) Decreases From X to Z
In case of  X Quality factor Is More , Impedance, Decreases From X to Z.

If the area of the TV telecast is to be doubled then what will be the height of the transmitting antenna ?

1

(a)

doubled

Does refraction in a water tank make apparent depth same throughout?

1

(a)

Ans. No Apparent depth is maximum for that part of the bottom of the tank which is observed normally. Apparent depth decreases with increasing obliquity. Due to this unequal refraction, the flat bottom of the tank appears concave.

A photon and an electron have been same de-Broglie wavelength which one has higher total energy?

1

(a)

Total energy of an electron E_e=mc²
Total energy of a photon, \(E_{p}=\frac{h c}{\lambda}\)
de-Broglie wavelength of electron of mass m moving with velocity V
\(\lambda=\frac{h}{m v}\)
\(\Rightarrow \ m=\frac{h}{\lambda v}\)
\(\therefore \text { Energy of an electron, } E_{e}=m c^{2}=\frac{h c^{2}}{\lambda v}\)
\(\therefore \ \frac{E_{e}}{E_{p}}=\frac{\frac{h c^{2}}{\lambda v}}{\frac{h c}{\lambda}}=\frac{c}{v}\)
As c > > v, therefore the total energy of electron is more than the total energy of photon.

Imagine removing one election from He⁴ and He³.Their energy levels, as worked out on the basis of Bohr's model will be very close. Explain why?

1

(a)

On removing one electron from He⁴ and He³, the energy levels, as worked out on the basis of Bohr's model will be very close as both the nuclei are very heavy as compared to electron mass. Also, after removing one electron, He⁴ and He³ atoms contain one electron and are hydrogen like atoms.

Establish the relationship between half life of a radio- active substance and decay constant

1

(a)

At t = T ½ N = No / 2 Using N = No e- \(\lambda \)t
No / 2 = No e ^{-\(\lambda \)t ½}
Solving we get, T1/2 = ln2/\(\lambda \) = 0.693/ \(\lambda \)

In a given diagram ,is the diode reverse (or) forward biased?

1

(a)

Reverse biased