Browse by Stream
QnA
Home

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A battery is connected between two points A and B in the circumference of a uniform conducting ring. AB of the ring subtends an angle <img alt="\theta" src="https://entrancecorner.oncodecogs.c

A battery is connected between two points A and B in the circumference of a uniform conducting ring. AB of the ring subtends an angle \theta at the centre. The value of the magnetic induction at the centre due to the current in the ring is:

 

Option: 1

Zero, only if \theta = 180\degree


Option: 2

Zero, for all values of \theta


Option: 3

Proportional to 2(180 - \theta)


Option: 4

Inversely proportional to r


Answers (1)

best_answer

The field due to the arc at the centres is given by:

                B = \frac{\mu_{0}i}{4\pi r} \phi

\therefore B _{net}= \frac{\mu_{0}i_{1} \theta}{4\pi r} (\cdot) + \frac{\mu_{0}i _{2}(2\pi - \theta)}{4\pi r} (\times)

B _{net}= V_{A} - V_{B} = i1R1 = i2R2

\implies i2 = i1\frac{R1}{R2}

            i2 = i1\frac{L1}{L2}                [\therefore L = r\theta] (arc length)

            i2 = \frac{i1 \theta }{2\pi - \theta}

\therefore B _{net}= \frac{\mu_{0}i_{1} \theta}{4\pi r} (\cdot) + \frac{\mu_{0}i _{1}\theta}{4\pi } (\times) = 0

 

i.e., the field at the centre of the coil is zero and is independent of \theta.

Posted by

rishi.raj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 April 8 Exam Analysis: Maths easier than before, inorganic chemistry gets fewer questions
anam-khan

Pawan Kalyan orders probe if his convoy delayed JEE Students
anam-khan

JEE Mains 2025 April 7 shift 2 maths section ‘lengthiest’; physics, chemistry easy

Latest Question