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Moving Charges and Magnetism — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism2 Marks
Question
Two long straight parallel wires A and B separated by a distance d, carry equal current I flowing in same direction as shown in the figure.
  1. Find the magnetic field at a point P situated between them at a distance x from one wire.
  2. Show graphically the variation of the magnetic field with distance x for 0 < x < d.
✓

Answer

  1. $\text{B}_\text{P}=\text{B}_\text{A}+\text{B}_\text{B}=\frac{\mu_0\text{I}}{2\pi\text{x}}(\text{upwards})+\frac{\mu_0\text{I}}{2\pi(\text{fx)}}(\text{down)}$
$=\frac{\mu_0\text{I}}{2\pi}\Big[\frac{1}{\text{x}}-\frac{1}{\text{d}-\text{x}}\Big]$
$=\frac{\mu_0\text{I}}{2\pi}\Big[\frac{\text{d}-\text{x}-\text{x}}{\text{x}(\text{d}-\text{x)}}\Big]$
$=\frac{\mu_0\text{I}}{2\pi}\Big(\frac{\text{d}-2\text{x}}{\text{x}(\text{d}-\text{x)}}\Big)\text{upwards}+\frac{\mu_0\text{I}}{2\pi(\text{d}-\text{x})}(\text{down})$
$(1)\div(2)$
$\Rightarrow\frac{\text{mv}^2_\text{n}\text{r}_\text{n}}{\text{mv}_\text{n}\text{r}_\text{n}}=\Big(\frac{\text{ze}^2}{4\pi\varepsilon_0}\Big)\Big(\frac{2\pi}{\text{nh}}\Big)$
$\Rightarrow\text{speed of }\text{e}^-,$
As $\text{B}_\text{A}>\text{B}_\text{B}$
  1.  

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