Electromagnetic Induction - Quiz 3

Electromagnetic induction : 3

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Q1.  Two concentric and coplanar coils have radii a and b(≫a) as shown in fig. Resistance of the inner coil is R. Current in the outer is increased from 0 to i, then the total change circulating the inner coil is

•  (μ₀ ia² π)/2Rb
•   (μ₀ iab)/2R
•  (μ₀ iab)/2a (πb²)/R
•  (μ₀ ib)/2πR

Solution
a

Q2.A wire is bent to form the double loop shown in figure. There is s uniform magnetic field directed into the plane of the loop. If the magnitude of this filed is decreasing, the current will flow from

•   a to b and c to d
•  b to a and d to c
•  a to b and d to c
•  b to a and c to d

Solution
c

Q3.  23. A metallic wire is folded to form a square loop of side a. It carries a current i and is kept perpendicular to0 the region of uniform magnetic filed B. If the shape of the loop is changed from square to an equilateral triangle without changing the length of the wire and current, the amount of work done in doing so is

•  Bia² (1-(4√3)/9)
•  Bia² (1-√3/9)
•  2/3 Bia²
•  Zero

Solution
a

Q4.  Two identical conducting rings A and B of radius R are rolling over a horizontal conducting plane with same speed v but in opposite direction. A constant magnetic filed B is present pointing into the plane of paper. Then the potential difference between the highest points of the two rings is

•  0
•  2BvR
•  4BvR
•  None of these

Solution
c

Q5.The capacitor of an oscillatory circuit of frequency 10,000 Hz is enclosed in a container. When the container is evacuated, the frequency changed by 50 Hz, the dielectric constant of the gas is

•  (μ₀1.1
•  (μ₀1.01)
•  (μ₀1.001)
•  1.0001

Solution
 b

Q6. A small square loop of wire of side l is placed inside a large square loop of wire of side L(L≫l). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

•  l/L
•  l²/L
•  L/l
•  L²/l

Solution
b

Q7.In an LR circuit connected to a battery, the rate at which energy is stored in the inductor is plotted against time during the growth of current in the circuit. Which of the following best represents the resulting curve?

• 

 

 

 

Solution
a

Q8.The inductance L of a solenoid of length l, whose windings are made of material of density D and resistivity ρ, is (the winding resistance is R)

•  μ₀/4πl Rm/(ρ D)
•  Tμ₀/4πR lm/(ρ D)
•  μ₀/4πl (R² m)/(ρ D)
•  μ₀/2πR lm/(ρ D)

Solution
a

Q9.The magnitude flux density B us changing in magnitude at a constant rate dB/dt. A given mass m of copper, drawn into a wire of radius a and formed into a circular loop of radius r is placed perpendicular to the field B. The induced current in the loop is i. The resistivity of copper is ρ and density is d. The value of the induced current i is

•  m/2πρd dB/dt
•  m/(2πa² r) dB/dt
•  m/4πad dB/dt
•  m/4πρd dB/dt

Solution
d

Q10. A conducting ring of radius r and resistance R rolls on a horizontal surface with constant velocityv. The magnitude filed B is uniform and is normal to the plane of the loop. Choose the correct option

•  The inclined emf between O and Q is Brv
•  An induced current I=2Bvr/R flows in the clockwise direction
•  An included current I=2Bvr/R flows in the anticlockwise direction
•  No current flows

Solution
d