Electromagnetic Induction - Quiz 5

Electromagnetic induction : 5

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Q1.  A uniform magnitude filed exists in a region given by B ⃗=3i ̂+4j ̂+5k ̂. A rod of length 5 m along y-axis moves with a constant speed of 1 m/s along x axis. Then the induced emf in the rod will be

•   0
•  25 V
•  20V
•  15V

Solution
b

Q2.A wire of lengthl, mass m and resistance R slides without any friction down the parallel conducting rails of negligible resistance figure. The rails are connected to each other at the bottom by a resistanceless rail parallel to the wire so that the wire and the rails from a closed rectangular conducting loop. The plane of the rails makes an angle θ with the horizontal and a uniform vertical magnetic field of induction B exists throughout the region. Find the steady-state velocity of the wire

•   mg/R sin⁡θ/(B² l² cos²⁡θ )
•  mg/R sin²⁡θ/(B² l² cos²⁡θ )
•  (mgR sin⁡θ)/(B2 l² cos²⁡θ )
•  mgR sin²⁡θ/(B² l² cos⁡θ )

Solution
c

Q3.  A rectangular loop with a sliding conductor of length l is located in a uniform magnetic field perpendicular to the plane of the loop figure. The magnetic induction isB. The conductor has a resistanceR. The sides AB and CD have resistances R₁and R₂, respectively. Find the current through the conductor during its motion to the right with a constant velocity v

•  (Blv(R₁+R₂))/(R₁ (R₁+R₂))
•  (Bl² v)/(R₁+R₁ R₂ )
•  (Blv(R₁+R₂))/(R₁ R₂+R(R₁+R₂))
•  (Bl² v)/(R₁ R₂+R(R₁+R₂))

Solution
c

Q4.  A conductor AB of length l moves in xy plane with velocity v ⃗=v₀ (i ̂-j ̂). A magnetic field B ⃗=B₀ (i ̂+j ̂) exists in the region. The induced emf is

•  Zero
•  2B₀ lv₀
•  B₀ lv₀
•  √2 B₀ lv₀

Solution
a

Q5.A bar magnet was pulled away from a hollow coil A as shown in fig. As the south pole came out of the coil, the bar magnet next to hollow coil B experienced a magnetic force

•  To the right
•  To the left
•  Upwards
•  Equal to zero

Solution
 a

Q6.  A toroid is wound over a circular core. Radius of each turn is r and radius of toroid is R(≫r). The coefficient of self-inductance of the toroid is given by

•  L=(μ₀ Nr²)/(2 R)
•  L=(μ₀ Nr)/(2 R)
•  L=(μ₀ Nr²)/( R)
•  L=(μ₀ N² r²)/(2 R)

Solution
d

Q7. A copper rod is bent into a semi-circle of radius a and at ends straight parts are bent along diameter of the semi-circle and are passed through fixed. Smooth and conducting ring O and O^' as shown in figure. A capacitor having capacitance C is connected to the rings. The system is located in a uniform magnetic field of induction B such that axis of rotation OO^' is perpendicular to the field direction. At initial moment of time(t=0), plane of semi-circle was normal to the field direction and the semi-circle is set in rotation with constant angular velocityω. Neglect the resistance and inductance of the circuit. The current flowing through the circuit as function of time is

•  1/4 πω² a² CB cos⁡ωt
•  1/2 πω² a CB cos⁡ωt
•  1/4 πω² a² CB sin⁡ωt
•  1/2 πω² a² CB sin⁡ωt

Solution
b

Q8. A semicircular wire of radius R is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strengthB. The induced emf between the ends is

•   BωR²/2
•  T2BωR²
•  Is variable
•  None of these

Solution
b

Q9.A square metal wire loop of side 10 cm and resistance 1 Ω is moved with constant velocity v₀ in a uniform magnetic field of induction B=2Wbm^-2, as shown in figure. The magnetic field lines are perpendicular to the plane of loop and directed into the paper. The loop is connected to the network of resistances, each of value 3 Ω. The resistance of the lead wires is negligible. The speed of the loop so as to have a steady current of 1 mA in the loop is

•  2 ms^-1
•  2 cms^-1
•  10 ms^-1
•  20 ms^-1

Solution
b

Q10. Three identical coils A,B and C carrying currents are placed coaxially with their planes parallel to one another. AandC carry currents as shown in figure B is kept fixed, while A and C both are moved towards B with the same speed. Initially, B is equally separated from Aand C. The direction of the inclined current in the coil B is

•  Same as that in coil A
•  Same as that in coil
•  Zero
•  None of these

Solution
c