A square loop of edge length 2 m carrying a current of 2 A is placed with its edges parallel to the x-y axis. A magnetic field is passing through the x-y plane and expressed as where . The net magnetic force experienced by the loop is ______ N.

Question

A square loop of edge length 2 m carrying a current of 2 A is placed with its edges parallel to the x-y axis. A magnetic field is passing through the x-y plane and expressed as $\vec{B} = B_{0} (1 + 4 x) \hat{k},$ where $B_{0} = 5 T .$ . The net magnetic force experienced by the loop is ______ N. [2024]

Smart Achievers · Accepted Answer

(160)

$B (x = 0) = B_{0}, B (x = 2) = 9 B_{0}$

Also, $\vec{F} = i \vec{ℓ} \times \vec{B}$

${\vec{F}}_{1} = i ℓ B_{0} (\hat{j} \times \hat{k}) = i ℓ B_{0} (\hat{i}) = 2 \times 2 \times 5 (\hat{i}) = 20 N (\hat{i})$

${\vec{F}}_{2} = 9 i ℓ B_{0} (- \hat{j} \times \hat{k}) = 9 i ℓ B_{0} (- \hat{i}) = 2 \times 2 \times 45 (- \hat{i}) = 180 N (- \hat{i})$

$F_{net} on AD and CB = 0$

${\vec{F}}_{net} = {\vec{F}}_{2} - {\vec{F}}_{1} = 160 N (- \hat{i})$

$\Rightarrow F_{net} = 160 N$

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Solution

Q. A square loop of edge length 2 m carrying a current of 2 A is placed with its edges parallel to the x-y axis. A magnetic field is passing through the x-y plane and expressed as B→=B0(1+4x)k^, where B0=5T.. The net magnetic force experienced by the loop is ______ N. [2024]

Ans. (160) B(x=0)=B0, B(x=2)=9B0 Also, F→=iℓ→×B→ F→1=iℓB0(j^×k^)=iℓB0(i^)=2×2×5(i^)=20N(i^) F→2=9iℓB0(-j^×k^)=9iℓB0(-i^)=2×2×45(-i^)=180N(-i^) Fnet on AD and CB=0 F→net=F→2-F→1=160N(-i^) ⇒Fnet=160N

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