Electromagnetic Induction | Physics JEE Main questions with Solutions

Q 1 :
A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and the angle of dip is 30°. The emf induced across the blades is $N π \times 10^{- 5}$ V. The value of N is ______. [2024]

0%

(32)

Q 2 :
A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $0.60 \times 10^{- 4}$ $W b m^{- 2}$ . The instantaneous value of emf induced in the wire when its velocity is $10 m s^{- 1}$ is _____ $\times 10^{- 3}$ V. [2024]

0%

(3) $B_{H} = 0.60 \times 10^{- 4} {Wb / m}^{2}$

$ε = B_{H} v l = 0.60 \times 10^{- 4} \times 10 \times 5$

$= 3 \times 10^{- 3} V$

Q 3 :
A rod of length 60 cm rotates with a uniform angular velocity 20 rad $s^{- 1}$ about its perpendicular bisector, in a uniform magnetic field 0.5 T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ______ V. [2024]

0%

(0)

$V_{B} - V_{C} = \frac{B_{0} ω l^{2}}{8}$

$V_{A} - V_{C} = \frac{B_{0} ω l^{2}}{8}$

$V_{B} - V_{A} = 0$

Q 4 :
A square loop PQRS having 10 turns, area $3.6 \times 10^{- 3} m^{2}$ and resistance 100 $Ω$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ___ $\times 10^{- 6} J$ . [2024]

0%

(3)

$W = heat loss$

$= \frac{Δ ϕ^{2}}{R Δ t} = \frac{{(3.6 \times 10^{- 3} \times 0.5 \times 10)}^{2}}{100 \times 1}$

$= \frac{18^{2}}{100} \times 10^{- 6} = 3.24 \times 10^{- 6} J$

Q 5 :
A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the x-axis and y-axis respectively, moves with a velocity of 5 cm/s in the positive x-axis direction, in a space containing a variable magnetic field in the positive z-direction. The field has a gradient of $10^{- 3}$ T/cm along the negative x-direction and it is decreasing with time at the rate of $10^{- 3}$ T/s. If the resistance of the loop is 6 $mΩ$ , the power dissipated by the loop as heat is ______ $\times 10^{- 9}$ W. [2024]

0%

(216)

$B_{0} is the magnetic field at origin$

$\frac{d B}{d x} = - \frac{10^{- 3}}{10^{- 2}} \Rightarrow \int_{B_{0}}^{B} d B = - \int_{0}^{x} 10^{- 1} d x$

$B - B_{0} = - 10^{- 1} x \Rightarrow B = (B_{0} - \frac{x}{10})$

$Motional emf in A B = 0$

$Motional emf in C D = 0$

$Motional emf in A D = ε_{1} = B_{0} l v$

$Magnetic field on rod B C,$

$B = (B_{0} - \frac{(- 12 \times 10^{- 2})}{10})$

$Motional emf in B C = ε_{2} = (B_{0} + \frac{12 \times 10^{- 2}}{10}) l \times v$

$ε_{eq} = ε_{2} - ε_{1} = 300 \times 10^{- 7} V$

$For time variation$

$(ε_{eq})' = A \frac{d B}{d t} = 60 \times 10^{- 7} V$

$(ε_{eq})_{net} = ε_{eq} + (ε_{eq})' = 360 \times 10^{- 7} V$

$Power = \frac{{(ε_{eq})}_{n e t}^{2}}{R} = 216 \times 10^{- 9} W$

Q 6 :
A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $10 π {rads}^{- 1}$ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ( $π$ = 3.14) [2025]

0.0628 V
0.5024 V
0.2512 V
0.1256 V

1

2

3

4

(3)

Given : B = 0.4 T, r = 20 cm and $ω = 10 π$ rad/s

The potential difference developed between the axis of the disc and the rim, $e = \frac{1}{2} B ω r^{2}$ = 0.2512 V

Q 7 :
Figure

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is $E \infty t^{n}$ , then value of n is ______. [2025]

0%

1

Figure

$E = l v B$

$E = \frac{2 x}{\sqrt{3}} \times v B and x = v t$

$E = \frac{2}{\sqrt{3}} v^{2} B t E \infty t^{1}$

Q 8 :
Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV. [2025]

Figure

0%

10

As field is uniform, we can replace the bent wire with straight wire from A to E. EMF $ε = B v l$

$ε = \frac{1}{\sqrt{2}} \times \frac{10}{100} \times \frac{2 (10 \sin 45 °)}{100} = 0.01 V = 10 mV$

Topic Question Set

Q 1 :
A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and the angle of dip is 30°. The emf induced across the blades is $N π \times 10^{- 5}$ V. The value of N is ______. [2024]

0%

0%

Q 3 :
A rod of length 60 cm rotates with a uniform angular velocity 20 rad $s^{- 1}$ about its perpendicular bisector, in a uniform magnetic field 0.5 T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ______ V. [2024]

0%

Q 4 :
A square loop PQRS having 10 turns, area $3.6 \times 10^{- 3} m^{2}$ and resistance 100 $Ω$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ___ $\times 10^{- 6} J$ . [2024]

0%

0%

Q 7 :
Figure

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is $E \infty t^{n}$ , then value of n is ______. [2025]

0%

Q 8 :
Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV. [2025]

Figure

0%

Want Us to Email you About Special Offers & Updates?

Topic Question Set

Q 1 : A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and the angle of dip is 30°. The emf induced across the blades is Nπ×10-5 V. The value of N is ______. [2024]

0%

Q 2 : A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field 0.60×10-4 Wbm-2. The instantaneous value of emf induced in the wire when its velocity is 10ms-1 is _____ ×10-3 V. [2024]

0%

Q 3 : A rod of length 60 cm rotates with a uniform angular velocity 20 rad s-1 about its perpendicular bisector, in a uniform magnetic field 0.5 T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ______ V. [2024]

0%

Q 4 : A square loop PQRS having 10 turns, area 3.6×10-3m2 and resistance 100 Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ___ ×10-6J. [2024]

0%

0%

Q 7 : Figure A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E∞tn, then value of n is ______. [2025]

0%

Q 8 : Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of 12 Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV. [2025] Figure

0%

Want Us to Email you About Special Offers & Updates?

Q 1 :
A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and the angle of dip is 30°. The emf induced across the blades is $N π \times 10^{- 5}$ V. The value of N is ______. [2024]

Q 3 :
A rod of length 60 cm rotates with a uniform angular velocity 20 rad $s^{- 1}$ about its perpendicular bisector, in a uniform magnetic field 0.5 T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ______ V. [2024]

Q 4 :
A square loop PQRS having 10 turns, area $3.6 \times 10^{- 3} m^{2}$ and resistance 100 $Ω$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s is ___ $\times 10^{- 6} J$ . [2024]

Q 7 :
Figure

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is $E \infty t^{n}$ , then value of n is ______. [2025]

Q 8 :
Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV. [2025]

Figure