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CBSE Class 12 Physics 2025 All Sets Solved Paper

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Question : 3 of 16
Marks: +1, -0
A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field B=(0.4 mT)j^+(0.6 mT)k^\vec{B} = (0.4\ \mathrm{mT}) \hat{j} + (0.6\ \mathrm{mT}) \hat{k} is switched on, in the region. The force acting on the segment is
Solution:  
The forces on a current-carrying wire in a magnetic field is:
F=l(L×B)F = l(L \times B)
Given:
I = 0.5A, L=1i^cmB=(0.4mTj^+0.6mTk^)L = 1 \hat{i} \, \mathrm{cm} \quad B = (0.4 \mathrm{mT} \hat{j} + 0.6 \mathrm{mT} \hat{k})
Using cross product:
L×B=i^×(0.4j^+0.6k^)L \times B = \hat{i} \times (0.4 \hat{j} + 0.6 \hat{k})
Using vector cross-product rules:
i^×j^=k^,i^×k^=j^\hat{i} \times \hat{j} = \hat{k}, \quad \hat{i} \times \hat{k} = -\hat{j}
i^(0.4j^+0.6k^)=0.4k^0.6j^\hat{i} \propto (0.4 \hat{j} + 0.6 \hat{k}) = 0.4 \hat{k} - 0.6 \hat{j}
Multiply by I = 0.5:
F=(0.2k^0.3j^)\overline{F} = (0.2 \hat{k} - 0.3 \hat{j})
Length was in cm and magnetic field in mT.
So, in SI unit F=(0.2k^0.3j^)×105N\vec{F} = (0.2 \hat{k} - 0.3 \hat{j}) \times 10^{-5} \, \mathrm{N}
F=(2k^3j^)μN\vec{F} = (2 \hat{k} - 3 \hat{j}) \, \mu \mathrm{N}
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