Question

Two long parallel wires A and B separated by a distance d, carry currents $i_1$ and $i_2$ respectively in the same direction. Write the following steps in a sequential order to find the magnitude of the resultant magnetic field at a point 'P', which is between the wires and is a distance '$x$' from the wire A.
(All the physical quantities are measured in SI units)
(a) Note the given values of $i_1,i_2$, $d$ and $x$.
(b) Write the formula to find the magnetic field due to a long straight current carrying wire i.e. $B=\frac{{\mu }_{0}i}{2\pi r}$
(c) Find the directions of the magnetic field at 'P' due to two wires A and B, using right hand thumb rule.
(d) Determine the magnetic field at P due to wire A, using $B_1=\frac{{\mu }_0{i}_1}{2\pi x}$
(e) If the directions of magnetic field are same, then the resultant magnitude is equal to the sum of $B_1$ and $B_2$.
(f) Determine the magnetic field $B_2$ due to wire B at point P, ie. $B_2=\frac{{\mu }_o{i}_2}{2\pi (d-x)}$
(g) If the directions of magnetic fields are opposite to each other, then the resultant magnitude is equal to the difference of $B_1$ and $B_2$.

• A. $dfcegba$
• B. $cdfegba$
• C. $acbdfeg$
• D. $abdfceg$

Answer 1

Answer: (D)

$abdfceg$

Note the given values of $i_1,i_2,d$ and $x$ (a).

Write the formula to find the magnetic field due to a long straight current carrying wire i.e. $B=\frac{{\mu }_{o}i}{2\pi r}$ (b).

Determine the magnetic field at P due to wire A, using $B_1=\frac{{\mu }_o{i}_1}{2\pi r}$ Determine $B_2$ due to wire B i.e., B ie, $B_2=\frac{{\mu }_o{i}_2}{2\pi (d-x)}$(f).

Find the directions of the magnetic field at 'P' due to two wires A and B, using right hand thumb rule (c).

If the directions of magnetic fields are same, then the resultant magnitude is equal to the sum of $B_1$ and $B_2$(e).

If the directions of the two magnetic fields are opposite, then the resultant magnitude is equal to the difference of $B_1$ and $B_2$ (g).