Electrodynamics and Maxwell's
Equations
By: Ayush Sekhari
(MM:30 , TIME:40 minutes)
OBJECTIVE QUESTIONS:
Every question in part 1 is 2 marks each. Every question in part 2 is 3 marks each.
PART 1
1) In which of the following cases is the mutual induction between the two wire loops zero?
2) Which of the following formulas is correct? (multiple answers may be true)
a) J=ne
b)
c)
( in some cases it may be equal but in general it isn’t.)
d)
J
3) A metal bar of mass m slides without friction on two parallel conducting rails a distance l apart. A
resistor R is connected across the rails and a uniform magnetic
field B, pointing into the page, fills the entire region.
Then which of the following is true:
(a) the current flows in the clockwise direction
(b) the current flowing is Bvl/R
(c) the current flows without any potential difference
(d) the potential difference doubles if the thickness of the moving bar is doubled
PART 2:
4) Consider two wires of equal cross section area one made of copper and the other made of
iron.(since these are two different materials so they have different conductivities) the two wires are
joined together and constant current is passed through them. Then in the common area of crosssection, the net charge:
a) there is no charge at the common cross-section area.
B) increases with time
c) decreases with time
d) remains constant with time.
5) Magnetic field through a loop varies as shown in the figure. Positive magnetic field implies that
the field lines come out of the plane (magnetic field is perpendicular to the plane of the loop and
assume anticlockwise current as positive).
For the above plot, which of the following represent the correct variation of current with time:
(a)
(b)
I
I
t
(c)
t
(d)
I
I
t
t
6) Which of the following is the correct match:
Quantity
unit
1:Capacitance
a:henry
2:Inductance
b:weber
3:Magnetic field
c:farads
4:flux
d:gauss
(a) 1 – a , 2 – c , 3 – b , 4 - d
(b) 1 – a , 2 – c , 3 – d , 4 - b
(c) 1 – c , 2 – a , 3 – d , 4 - b
(d) 1 – c , 2 – a , 3 – b , 4 - d
PART 3:
7)Two metal objects are embedded in weakly conducting material of conductivity u (as shown in the
figure). Show that the resistance between them is related to the capacitance of the arrangement by
[4 marks]
8)A long solenoid with radius a and n turns per unit length carries a time-dependent current I(t) in
the positive Φ direction. Find the electric field (magnitude and direction) at a distances from the axis
(both inside and outside the solenoid), in the quasistatic approximation.
[5 marks]
9)A long coaxial cable carries current I (the current flows down the surface of the inner cylinder,
radius a, and back along the outer cylinder, radius b) as shown in Figure. Find the magnetic energy
stored in a section of length l. Hence find the inductance per unit length of the cable.
(hint: use the fact that magnetic energy stored = L )
[4+2 marks]