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Physics · 2025 · 3 marks
CBSE 2025 · Region 4 · Set 3 · Q23
(a) In which cases does a charged particle not experience a force in a magnetic field? (b) A square loop MNPK of side ' l ' carrying a current ' I_2…
(a)
In which cases does a charged particle not experience a force in a magnetic field?
(b)
A square loop MNPK of side ' $\displaystyle l$ ' carrying a current ' $\displaystyle \mathrm{I}_{2}$ ' is kept close to a long straight wire in the same plane and the wire carries a steady current $\displaystyle \mathrm{I}_{1}$ as shown in the figure. Obtain the magnitude of magnetic force exerted by the wire on the loop.
Marking-scheme solution
(a)
If the charged particle is at rest, $\displaystyle v=0$.
If $\displaystyle \vec{B}$ is parallel or antiparallel to $\displaystyle \vec{v}$.
(b)
Magnitude of force acting between two current carrying conductors:
$\displaystyle F=\frac{\mu_{0}}{4 \pi} \frac{2 I_{1} I_{2}}{r} L$
Force on segment MN of loop:
$\displaystyle F_{M N}=\frac{\mu_{0}}{4 \pi} \frac{2 I_{1} I_{2}}{l} \times l$ (towards the wire)
Force on segment KP of loop:
$\displaystyle F_{K P}=\frac{\mu_{0}}{4 \pi} \frac{2 I_{1} I_{2}}{2 l} \times l$ (away from the wire)
No force due to segments MK and NP.
Net force on the loop:
$\displaystyle F=F_{M N}-F_{K P}$
$\displaystyle F=\frac{\mu_{0}}{4 \pi} I_{1} I_{2}$
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