The wire shown is figure carries a current of 32 A. If r=3.14 cm, the magnetic field at point P will be

Question

The wire shown is figure carries a current of 32 A. If r=3.14 cm, the magnetic field at point P will be (A) 1.6 × 10-4 T (B) 3.2 × 10-4 T (C) 4.8 × 10-4 T (D) 6.4 × 10-4 T

Tardigrade Admin · Accepted Answer

Magnetic field due to a complete circular wire loop carrying a current

I

at the centre is

\frac{μ _{0} I}{2 r}

Here, the straight portions of the wire do not contribute because the point

P

is along them. The field at

P

is due to

\frac{3}{4}

th of the loop of radius

r

. Thus

B = \frac{3}{4} (\frac{μ _{0} I}{2 r})

= \frac{3}{4} \times \frac{4 π \times 1 0 ^{- 7} \times 32}{2 \times 314 \times 1 0 ^{- 7}}

= 4.8 \times 1 0^{- 6} T

Q. The wire shown is figure carries a current of $32 A$ . If $r = 3.14 c m$ , the magnetic field at point $P$ will be

$1.6 \times 1 0^{- 4} T$

$3.2 \times 1 0^{- 4} T$

$4.8 \times 1 0^{- 4} T$

$6.4 \times 1 0^{- 4} T$

Q. The wire shown is figure carries a current of 32A. If r=3.14cm, the magnetic field at point P will be

1.6×10−4T

3.2×10−4T

4.8×10−4T

6.4×10−4T

Q. The wire shown is figure carries a current of $32 A$ . If $r = 3.14 c m$ , the magnetic field at point $P$ will be

$1.6 \times 1 0^{- 4} T$

$3.2 \times 1 0^{- 4} T$

$4.8 \times 1 0^{- 4} T$

$6.4 \times 1 0^{- 4} T$