Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A magnet of length 10 cm and magnetic moment 1 Am, is placed along the side A B of an equilateral triangle ABC. If the length of side A B is 10 cm, the magnetic field at point C is</

A magnet of length 10 cm and magnetic moment 1 Am, is placed along the side A B of an equilateral triangle ABC. If the length of side A B is 10 cm, the magnetic field at point C is

Option: 1

10^{-9} \mathrm{~T}


Option: 2

10^{-7} \mathrm{~T}


Option: 3

10^{-5} \mathrm{~T}


Option: 4

10^{-4} \mathrm{~T}


Answers (1)

best_answer

Let m be the pole strength of each pole of the magnet . The magnetic field at C due to the \mathrm{N} -pole is given by

\mathrm{B_1=\frac{\mu_0}{4 \pi} \frac{m}{(A C)^2}}

direction along A C away from C.

The magnetic field at C due to the S-pole is given by

\mathrm{B_2=\frac{\mu_0}{4 \pi} \cdot \frac{m}{(B C)^2} }
directed along C B towards B.

Since \mathrm{ A C=B C, B_1=B_2 }. The resultant magnetic field at C is given by

\mathrm{B^2 =B_1^2+B_2^2+2 B_1 B_2 \cos 120^{\circ} \\ }

\mathrm{ =B_1^2+B_2^2-B_1 B_2 \\ }

\mathrm{ =B_1^2+B_2^2-B_1 B_2 \\ =2 B_1^2-B_1^2=B_1^2 \quad\left(\because B_2=B_1\right) }

or

\mathrm{ B=B_1 =\frac{\mu_0 m}{4 \pi(A C)^2}=\frac{\mu_0 m}{4 \pi a^2} \\ }

\mathrm{ =\frac{\mu_0}{4 \pi} \cdot \frac{(m a)}{a^3}=\frac{\mu_0}{4 \pi} \cdot \frac{M}{a^3} }

Given:  \mathrm{ M=1 \mathrm{~A} \mathrm{~m}^2, a=10 \mathrm{~cm}=0.1 \mathrm{~m} }  Also \mathrm{ \mu_0= 4~ \pi \times 10^{-7} \mathrm{~T} \mathrm{~A}^{-1} \mathrm{~m} } 

Substituting these values in (1), we get  \mathrm{B=10^{-4} \mathrm{~T} } which is option (d).

Posted by

Pankaj Sanodiya

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

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question