A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by [2023]

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Q.
A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by [2023]

1 $\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed away from page

2 $\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed into the page

3 $\frac{μ_{0} i}{4 R}$ pointed into the page

4 $\frac{μ_{0} i}{4 R}$ pointed away from the page

Ans.
(1)

$B_{p}$ due to wire $1 = \frac{μ_{0} i}{4 π R} \otimes$

$B_{p}$ due to wire $3 = \frac{μ_{0} i}{4 π R} \otimes$

$B_{p}$ due to wire $2 = \frac{μ_{0} i}{4 R} ⊙$

$B_{net} = - \frac{μ_{0} i}{2 π R} + \frac{μ_{0} i}{4 R} = \frac{μ_{0} i}{4 R} [- \frac{2}{π} + 1] = \frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$

Pointed away from page.

Solution

Q.
A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by [2023]

1 $\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed away from page

2 $\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed into the page

3 $\frac{μ_{0} i}{4 R}$ pointed into the page

4 $\frac{μ_{0} i}{4 R}$ pointed away from the page

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Solution

Q. A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by [2023]

1 μ0i4R[1-2π] pointed away from page

2 μ0i4R[1-2π] pointed into the page

3 μ0i4R pointed into the page

4 μ0i4R pointed away from the page

Ans. (1) Bp due to wire 1=μ0i4πR ⊗ Bp due to wire 3=μ0i4πR ⊗ Bp due to wire 2=μ0i4R ⊙ Bnet=-μ0i2πR+μ0i4R=μ0i4R[-2π+1]=μ0i4R[1-2π] Pointed away from page.

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Q.
A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by [2023]

1 $\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed away from page

2 $\frac{μ_{0} i}{4 R} [1 - \frac{2}{π}]$ pointed into the page

3 $\frac{μ_{0} i}{4 R}$ pointed into the page

4 $\frac{μ_{0} i}{4 R}$ pointed away from the page