A steady current I goes through a w...
Question

# A steady current I goes through a wire loop PQR having shape of a right angle triangle with ( mathrm{PQ}=3 mathrm{x} )( P R=4 x ) and ( Q R=5 x . ) If the magnitude of the magnetic field at ( P ) due to this loop is ( kleft(frac{mu_{0} I}{48 pi x}right), ) find the value of ( k )

NEET/Medical Exams
Physics
Solution
221
4.0 (1 ratings)

[
B=frac{u_{0}}{4 pi} frac{I}{P M}left(cos theta_{1}+omegaleft(theta_{2}right)-dot{i}right)
]
( operatorname{in} Delta operatorname{Pes} M )
[
9 x^{2}=p m^{2}+a^{2}-(i i)
]
[
begin{array}{l}
text { in } Delta P R m
16 x^{2}=P m^{2}+(5 x-a)^{2}-(iii)
=7 x^{2}=25 x^{2}-10 x a
end{array}
end{array}
]
from ( (ddot{i} i) ) and ( (i v) )
[
begin{aligned}
9 x^{2} &=p m^{2}+(1 cdot 8 x)^{2}
P m &=sqrt{9 x^{2}-3 cdot 24 x^{2}}
&=sqrt{5 cdot 76 x^{2}}=2 cdot 4 x
end{aligned}
]
( Also quad cos theta_{1}=frac{5 x-a}{4 x} )
[
begin{array}{l}
begin{aligned}
&=frac{5 x-1.8 x}{4 x}
&=frac{3.2}{4}=0.8
end{aligned}
begin{aligned}
B=& frac{u_{0}}{u pi} times frac{I}{2.4 x}(0.6+0.8)
&=left[frac{U_{0} I}{48 pi x}right] 7
end{aligned}
end{array}
]

So  k =7