Question

Q3.
A
A wire of radius 0.5cm carries a current of 100A
which is informly distributed over its cross-
section find the magretic field
at 0.1cm from the axis of the wire.​

Answer 1

Explanation:

Ampere circuit law

B×2πr=λ

w

I

a=3.0mm=3×10

−3

I= total current enclosed

in the area of circle of radius r

I=

m

2

100mp

(a) area circule of radius r=2.0mm=2×10

−3

m will be A=AR

2

=4π×10

−6

m

2

⇒ current I=IA=100×4π×10

−6

amp

so field wire will be given by

B×2πr=λ

w

I=λ

0

×4π×10

−6

×100

⇒B=

r

2λ

w

×10

−4

=

2×10

−3

2×4π×10

−11

Tesla

putting (λ

w

=4π×10

−7

) m.k.s unit

or

B=4π×10

−8

Tesla

(b) area circle of radiusr=4.0mm

which is more than radius of wire (a=3mm)

so current =total current

=3×π(3×10

−3

)

2

=9π×10

−4

field

B=

2πr

λ

0

I

=

2π× 4×10

−3

4π×10

−7

×9π×10

−4

2

9π

×10

−8

Tesla