358615
A conducting circular loop is placed in a uniform magnetic field of induction \(B\) tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate \((dr/dt)\). Then the induced e.m.f at the instant when the radius \(r\) is:
If the radius is \(r\) at a time \(t\), then the intantaneous magnetic flux \(f\) is given by: \(\phi=\pi r^{2} B\) Now, induced e.m.f. \(\varepsilon\) is given by \(\begin{aligned}& \varepsilon=-\dfrac{d \phi}{d t}=-\dfrac{d}{d t}\left(\pi r^{2} B\right)=\pi B\left(2 r \dfrac{d r}{d t}\right) \\& \varepsilon=2 \pi r B\left(\dfrac{d r}{d t}\right)\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358616
A conducting circular loop is placed in a uniform magnetic field \(0.04 T\) with its plane perpendicular to the magnetic field. The radius of the loop startsshrinking at \(2\;\,mm\;{s^{ - 1}}\). The indu ced emf in the loop when the radius is \(2\;\,cm\) is
1 \(3.2\pi \mu V\)
2 \(1.6\pi \mu V\)
3 \(4.8\pi \mu V\)
4 \(0.8\pi \mu V\)
Explanation:
Magnetic field, \(B=0.04 T\) and rate of change of radius of coil due to shrinkage, \(\dfrac{-d r}{d t}=2 m \mathrm{~ms}^{-1}\) induced emf, \(\varepsilon=\dfrac{-d \phi}{d t}=-B \dfrac{d A}{d t}=-B \pi 2 r \dfrac{d r}{d t}\) Now, if \(r = 2\;\,cm\) \(\varepsilon=0.04 \times \pi \times 2 \times 2 \times 10^{-2} \times 2 \times 10^{-3}\) \( = 3.2\,\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358617
A conducting circular loop is placed in a uniform magnetic field, \(B=0.025 T\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\,mm{s^{ - 1}}\). The induced emf when the radius is \(2\;\,cm\), is
1 \(2 \pi \mu V\)
2 \(\pi \mu V\)
3 \(\dfrac{\pi}{2} \mu V\)
4 \(2 \mu V\)
Explanation:
Magnetic flux \(\phi\) linked with magnetic field \(B\) and area \(A\) is given by \(\phi=B \cdot A=|B||A| \cos \theta\left(\theta=0^{\circ}\right)\) So, \(\phi=B A=B \pi r^{2}\) Induced emf, \(|\varepsilon|=\left|\dfrac{-d \phi}{d t}\right|=B \pi(2 r) \dfrac{d r}{d t}\) \(=0.025 \times \pi \times 2 \times 2 \times 10^{-2} \times 1 \times 10^{-3}=\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358618
The magnetic flux linked with a coil satisfies the realtion \(\phi = \left( {4{t^2} - 6t + 9} \right)Wb,\) where \(t\) is the time in second. The emf induced in the coil at \(t = 2\;s\) is:
1 \(22\;V\)
2 \(18\;V\)
3 \(16\;V\)
4 \(40\;V\)
Explanation:
Given, \(\phi=4 t^{2}+6 t+9\) and \(t = 2\;\,s\) We know that \(|\varepsilon|=\left|\dfrac{d \phi}{d t}\right|\) Here, \(\left|\dfrac{d \phi}{d t}\right|=|8 t+6| \Rightarrow\left(\dfrac{d \phi}{d t}\right)_{t=2}=8 \times 2+6\) Induced emf in the coil \( = 22\;\,V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358619
Assertion : Induced \(e.m.f.\) depends on number of turns in coil and area of the coil both associated with changing magnetic flux. Reason : Induced \(e.m.f.\) decreases with increase in number of turns of coil.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The induced electromotive force \((e.m.f.)\) in a coil is directly related to the number of turns \((N)\) in the coil and the rate of change of magnetic flux, as defined by Faraday's law of electromagnetic induction. Increasing the number of turns in the coil results in a higher induced e.m.f. Assertion is true Reason is false So correct option is (3).
358615
A conducting circular loop is placed in a uniform magnetic field of induction \(B\) tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate \((dr/dt)\). Then the induced e.m.f at the instant when the radius \(r\) is:
If the radius is \(r\) at a time \(t\), then the intantaneous magnetic flux \(f\) is given by: \(\phi=\pi r^{2} B\) Now, induced e.m.f. \(\varepsilon\) is given by \(\begin{aligned}& \varepsilon=-\dfrac{d \phi}{d t}=-\dfrac{d}{d t}\left(\pi r^{2} B\right)=\pi B\left(2 r \dfrac{d r}{d t}\right) \\& \varepsilon=2 \pi r B\left(\dfrac{d r}{d t}\right)\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358616
A conducting circular loop is placed in a uniform magnetic field \(0.04 T\) with its plane perpendicular to the magnetic field. The radius of the loop startsshrinking at \(2\;\,mm\;{s^{ - 1}}\). The indu ced emf in the loop when the radius is \(2\;\,cm\) is
1 \(3.2\pi \mu V\)
2 \(1.6\pi \mu V\)
3 \(4.8\pi \mu V\)
4 \(0.8\pi \mu V\)
Explanation:
Magnetic field, \(B=0.04 T\) and rate of change of radius of coil due to shrinkage, \(\dfrac{-d r}{d t}=2 m \mathrm{~ms}^{-1}\) induced emf, \(\varepsilon=\dfrac{-d \phi}{d t}=-B \dfrac{d A}{d t}=-B \pi 2 r \dfrac{d r}{d t}\) Now, if \(r = 2\;\,cm\) \(\varepsilon=0.04 \times \pi \times 2 \times 2 \times 10^{-2} \times 2 \times 10^{-3}\) \( = 3.2\,\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358617
A conducting circular loop is placed in a uniform magnetic field, \(B=0.025 T\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\,mm{s^{ - 1}}\). The induced emf when the radius is \(2\;\,cm\), is
1 \(2 \pi \mu V\)
2 \(\pi \mu V\)
3 \(\dfrac{\pi}{2} \mu V\)
4 \(2 \mu V\)
Explanation:
Magnetic flux \(\phi\) linked with magnetic field \(B\) and area \(A\) is given by \(\phi=B \cdot A=|B||A| \cos \theta\left(\theta=0^{\circ}\right)\) So, \(\phi=B A=B \pi r^{2}\) Induced emf, \(|\varepsilon|=\left|\dfrac{-d \phi}{d t}\right|=B \pi(2 r) \dfrac{d r}{d t}\) \(=0.025 \times \pi \times 2 \times 2 \times 10^{-2} \times 1 \times 10^{-3}=\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358618
The magnetic flux linked with a coil satisfies the realtion \(\phi = \left( {4{t^2} - 6t + 9} \right)Wb,\) where \(t\) is the time in second. The emf induced in the coil at \(t = 2\;s\) is:
1 \(22\;V\)
2 \(18\;V\)
3 \(16\;V\)
4 \(40\;V\)
Explanation:
Given, \(\phi=4 t^{2}+6 t+9\) and \(t = 2\;\,s\) We know that \(|\varepsilon|=\left|\dfrac{d \phi}{d t}\right|\) Here, \(\left|\dfrac{d \phi}{d t}\right|=|8 t+6| \Rightarrow\left(\dfrac{d \phi}{d t}\right)_{t=2}=8 \times 2+6\) Induced emf in the coil \( = 22\;\,V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358619
Assertion : Induced \(e.m.f.\) depends on number of turns in coil and area of the coil both associated with changing magnetic flux. Reason : Induced \(e.m.f.\) decreases with increase in number of turns of coil.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The induced electromotive force \((e.m.f.)\) in a coil is directly related to the number of turns \((N)\) in the coil and the rate of change of magnetic flux, as defined by Faraday's law of electromagnetic induction. Increasing the number of turns in the coil results in a higher induced e.m.f. Assertion is true Reason is false So correct option is (3).
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
PHXII06:ELECTROMAGNETIC INDUCTION
358615
A conducting circular loop is placed in a uniform magnetic field of induction \(B\) tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate \((dr/dt)\). Then the induced e.m.f at the instant when the radius \(r\) is:
If the radius is \(r\) at a time \(t\), then the intantaneous magnetic flux \(f\) is given by: \(\phi=\pi r^{2} B\) Now, induced e.m.f. \(\varepsilon\) is given by \(\begin{aligned}& \varepsilon=-\dfrac{d \phi}{d t}=-\dfrac{d}{d t}\left(\pi r^{2} B\right)=\pi B\left(2 r \dfrac{d r}{d t}\right) \\& \varepsilon=2 \pi r B\left(\dfrac{d r}{d t}\right)\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358616
A conducting circular loop is placed in a uniform magnetic field \(0.04 T\) with its plane perpendicular to the magnetic field. The radius of the loop startsshrinking at \(2\;\,mm\;{s^{ - 1}}\). The indu ced emf in the loop when the radius is \(2\;\,cm\) is
1 \(3.2\pi \mu V\)
2 \(1.6\pi \mu V\)
3 \(4.8\pi \mu V\)
4 \(0.8\pi \mu V\)
Explanation:
Magnetic field, \(B=0.04 T\) and rate of change of radius of coil due to shrinkage, \(\dfrac{-d r}{d t}=2 m \mathrm{~ms}^{-1}\) induced emf, \(\varepsilon=\dfrac{-d \phi}{d t}=-B \dfrac{d A}{d t}=-B \pi 2 r \dfrac{d r}{d t}\) Now, if \(r = 2\;\,cm\) \(\varepsilon=0.04 \times \pi \times 2 \times 2 \times 10^{-2} \times 2 \times 10^{-3}\) \( = 3.2\,\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358617
A conducting circular loop is placed in a uniform magnetic field, \(B=0.025 T\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\,mm{s^{ - 1}}\). The induced emf when the radius is \(2\;\,cm\), is
1 \(2 \pi \mu V\)
2 \(\pi \mu V\)
3 \(\dfrac{\pi}{2} \mu V\)
4 \(2 \mu V\)
Explanation:
Magnetic flux \(\phi\) linked with magnetic field \(B\) and area \(A\) is given by \(\phi=B \cdot A=|B||A| \cos \theta\left(\theta=0^{\circ}\right)\) So, \(\phi=B A=B \pi r^{2}\) Induced emf, \(|\varepsilon|=\left|\dfrac{-d \phi}{d t}\right|=B \pi(2 r) \dfrac{d r}{d t}\) \(=0.025 \times \pi \times 2 \times 2 \times 10^{-2} \times 1 \times 10^{-3}=\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358618
The magnetic flux linked with a coil satisfies the realtion \(\phi = \left( {4{t^2} - 6t + 9} \right)Wb,\) where \(t\) is the time in second. The emf induced in the coil at \(t = 2\;s\) is:
1 \(22\;V\)
2 \(18\;V\)
3 \(16\;V\)
4 \(40\;V\)
Explanation:
Given, \(\phi=4 t^{2}+6 t+9\) and \(t = 2\;\,s\) We know that \(|\varepsilon|=\left|\dfrac{d \phi}{d t}\right|\) Here, \(\left|\dfrac{d \phi}{d t}\right|=|8 t+6| \Rightarrow\left(\dfrac{d \phi}{d t}\right)_{t=2}=8 \times 2+6\) Induced emf in the coil \( = 22\;\,V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358619
Assertion : Induced \(e.m.f.\) depends on number of turns in coil and area of the coil both associated with changing magnetic flux. Reason : Induced \(e.m.f.\) decreases with increase in number of turns of coil.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The induced electromotive force \((e.m.f.)\) in a coil is directly related to the number of turns \((N)\) in the coil and the rate of change of magnetic flux, as defined by Faraday's law of electromagnetic induction. Increasing the number of turns in the coil results in a higher induced e.m.f. Assertion is true Reason is false So correct option is (3).
358615
A conducting circular loop is placed in a uniform magnetic field of induction \(B\) tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate \((dr/dt)\). Then the induced e.m.f at the instant when the radius \(r\) is:
If the radius is \(r\) at a time \(t\), then the intantaneous magnetic flux \(f\) is given by: \(\phi=\pi r^{2} B\) Now, induced e.m.f. \(\varepsilon\) is given by \(\begin{aligned}& \varepsilon=-\dfrac{d \phi}{d t}=-\dfrac{d}{d t}\left(\pi r^{2} B\right)=\pi B\left(2 r \dfrac{d r}{d t}\right) \\& \varepsilon=2 \pi r B\left(\dfrac{d r}{d t}\right)\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358616
A conducting circular loop is placed in a uniform magnetic field \(0.04 T\) with its plane perpendicular to the magnetic field. The radius of the loop startsshrinking at \(2\;\,mm\;{s^{ - 1}}\). The indu ced emf in the loop when the radius is \(2\;\,cm\) is
1 \(3.2\pi \mu V\)
2 \(1.6\pi \mu V\)
3 \(4.8\pi \mu V\)
4 \(0.8\pi \mu V\)
Explanation:
Magnetic field, \(B=0.04 T\) and rate of change of radius of coil due to shrinkage, \(\dfrac{-d r}{d t}=2 m \mathrm{~ms}^{-1}\) induced emf, \(\varepsilon=\dfrac{-d \phi}{d t}=-B \dfrac{d A}{d t}=-B \pi 2 r \dfrac{d r}{d t}\) Now, if \(r = 2\;\,cm\) \(\varepsilon=0.04 \times \pi \times 2 \times 2 \times 10^{-2} \times 2 \times 10^{-3}\) \( = 3.2\,\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358617
A conducting circular loop is placed in a uniform magnetic field, \(B=0.025 T\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\,mm{s^{ - 1}}\). The induced emf when the radius is \(2\;\,cm\), is
1 \(2 \pi \mu V\)
2 \(\pi \mu V\)
3 \(\dfrac{\pi}{2} \mu V\)
4 \(2 \mu V\)
Explanation:
Magnetic flux \(\phi\) linked with magnetic field \(B\) and area \(A\) is given by \(\phi=B \cdot A=|B||A| \cos \theta\left(\theta=0^{\circ}\right)\) So, \(\phi=B A=B \pi r^{2}\) Induced emf, \(|\varepsilon|=\left|\dfrac{-d \phi}{d t}\right|=B \pi(2 r) \dfrac{d r}{d t}\) \(=0.025 \times \pi \times 2 \times 2 \times 10^{-2} \times 1 \times 10^{-3}=\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358618
The magnetic flux linked with a coil satisfies the realtion \(\phi = \left( {4{t^2} - 6t + 9} \right)Wb,\) where \(t\) is the time in second. The emf induced in the coil at \(t = 2\;s\) is:
1 \(22\;V\)
2 \(18\;V\)
3 \(16\;V\)
4 \(40\;V\)
Explanation:
Given, \(\phi=4 t^{2}+6 t+9\) and \(t = 2\;\,s\) We know that \(|\varepsilon|=\left|\dfrac{d \phi}{d t}\right|\) Here, \(\left|\dfrac{d \phi}{d t}\right|=|8 t+6| \Rightarrow\left(\dfrac{d \phi}{d t}\right)_{t=2}=8 \times 2+6\) Induced emf in the coil \( = 22\;\,V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358619
Assertion : Induced \(e.m.f.\) depends on number of turns in coil and area of the coil both associated with changing magnetic flux. Reason : Induced \(e.m.f.\) decreases with increase in number of turns of coil.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The induced electromotive force \((e.m.f.)\) in a coil is directly related to the number of turns \((N)\) in the coil and the rate of change of magnetic flux, as defined by Faraday's law of electromagnetic induction. Increasing the number of turns in the coil results in a higher induced e.m.f. Assertion is true Reason is false So correct option is (3).
358615
A conducting circular loop is placed in a uniform magnetic field of induction \(B\) tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate \((dr/dt)\). Then the induced e.m.f at the instant when the radius \(r\) is:
If the radius is \(r\) at a time \(t\), then the intantaneous magnetic flux \(f\) is given by: \(\phi=\pi r^{2} B\) Now, induced e.m.f. \(\varepsilon\) is given by \(\begin{aligned}& \varepsilon=-\dfrac{d \phi}{d t}=-\dfrac{d}{d t}\left(\pi r^{2} B\right)=\pi B\left(2 r \dfrac{d r}{d t}\right) \\& \varepsilon=2 \pi r B\left(\dfrac{d r}{d t}\right)\end{aligned}\)
PHXII06:ELECTROMAGNETIC INDUCTION
358616
A conducting circular loop is placed in a uniform magnetic field \(0.04 T\) with its plane perpendicular to the magnetic field. The radius of the loop startsshrinking at \(2\;\,mm\;{s^{ - 1}}\). The indu ced emf in the loop when the radius is \(2\;\,cm\) is
1 \(3.2\pi \mu V\)
2 \(1.6\pi \mu V\)
3 \(4.8\pi \mu V\)
4 \(0.8\pi \mu V\)
Explanation:
Magnetic field, \(B=0.04 T\) and rate of change of radius of coil due to shrinkage, \(\dfrac{-d r}{d t}=2 m \mathrm{~ms}^{-1}\) induced emf, \(\varepsilon=\dfrac{-d \phi}{d t}=-B \dfrac{d A}{d t}=-B \pi 2 r \dfrac{d r}{d t}\) Now, if \(r = 2\;\,cm\) \(\varepsilon=0.04 \times \pi \times 2 \times 2 \times 10^{-2} \times 2 \times 10^{-3}\) \( = 3.2\,\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358617
A conducting circular loop is placed in a uniform magnetic field, \(B=0.025 T\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1\,mm{s^{ - 1}}\). The induced emf when the radius is \(2\;\,cm\), is
1 \(2 \pi \mu V\)
2 \(\pi \mu V\)
3 \(\dfrac{\pi}{2} \mu V\)
4 \(2 \mu V\)
Explanation:
Magnetic flux \(\phi\) linked with magnetic field \(B\) and area \(A\) is given by \(\phi=B \cdot A=|B||A| \cos \theta\left(\theta=0^{\circ}\right)\) So, \(\phi=B A=B \pi r^{2}\) Induced emf, \(|\varepsilon|=\left|\dfrac{-d \phi}{d t}\right|=B \pi(2 r) \dfrac{d r}{d t}\) \(=0.025 \times \pi \times 2 \times 2 \times 10^{-2} \times 1 \times 10^{-3}=\pi \mu V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358618
The magnetic flux linked with a coil satisfies the realtion \(\phi = \left( {4{t^2} - 6t + 9} \right)Wb,\) where \(t\) is the time in second. The emf induced in the coil at \(t = 2\;s\) is:
1 \(22\;V\)
2 \(18\;V\)
3 \(16\;V\)
4 \(40\;V\)
Explanation:
Given, \(\phi=4 t^{2}+6 t+9\) and \(t = 2\;\,s\) We know that \(|\varepsilon|=\left|\dfrac{d \phi}{d t}\right|\) Here, \(\left|\dfrac{d \phi}{d t}\right|=|8 t+6| \Rightarrow\left(\dfrac{d \phi}{d t}\right)_{t=2}=8 \times 2+6\) Induced emf in the coil \( = 22\;\,V\)
PHXII06:ELECTROMAGNETIC INDUCTION
358619
Assertion : Induced \(e.m.f.\) depends on number of turns in coil and area of the coil both associated with changing magnetic flux. Reason : Induced \(e.m.f.\) decreases with increase in number of turns of coil.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
The induced electromotive force \((e.m.f.)\) in a coil is directly related to the number of turns \((N)\) in the coil and the rate of change of magnetic flux, as defined by Faraday's law of electromagnetic induction. Increasing the number of turns in the coil results in a higher induced e.m.f. Assertion is true Reason is false So correct option is (3).