SATHEE: Electromagnetic Induction and Alternating Current 5 Question 1

Electromagnetic Induction and Alternating Current 5 Question 1

1. A uniform but time-varying magnetic field $B (t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ from the centre of the circular region

$(2000, 2 M)$

(a) is zero

(b) decreases as $1 / r$

(d) decreases as $1 / r^{2}$

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Answer:

Correct Answer: 1. (b)

Solution:

$\int E \cdot d l = \frac{d φ}{d t} = S \frac{d B}{d t}$

$or E (2 π r) = π a^{2} \frac{d B}{d t}$

For $r \geq a$ ,

$∴ E = \frac{a^{2}}{2 r} \frac{d B}{d t}$

$∴$ Induced electric field $\propto 1 / r$

For $r \leq a$ ,

$\begin{aligned} E (2 π r) & = π r^{2} \frac{d B}{d t} \\ or & E & = \frac{r}{2} \frac{d B}{d t} \\ or & E & \propto r \\ At r = a, & E & = \frac{a}{2} \frac{d B}{d t} \end{aligned}$

Therefore, variation of $E$ with $r$ (distance from centre) will be as follows

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Electromagnetic Induction and Alternating Current 5 Question 1

1. A uniform but time-varying magnetic field $B (t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ from the centre of the circular region

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Electromagnetic Induction and Alternating Current 5 Question 1

1. A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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1. A uniform but time-varying magnetic field $B (t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ from the centre of the circular region