charge moving with velocity in the region of magnetic field The magnitude of force acting on it is . The value of is

Question

$1 μ C$ charge moving with velocity $\vec{v} = (\hat{i} - 2 \hat{j} + 3 \hat{k}) m/s$ in the region of magnetic field $\vec{B} = (2 \hat{i} + 3 \hat{j} - 5 \hat{k}) T .$ The magnitude of force acting on it is $\sqrt{α} \times 10^{- 6} N$ . The value of $α$ is ________. [2026]

Smart Achievers · Accepted Answer

(171)

$\vec{F} = q (\vec{v} \times \vec{B}) = 1 \times 10^{- 6}$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 2 & 3 \\ 2 & 3 & - 5 \end{matrix} |$

$\vec{F} = 10^{- 6} [\hat{i} + 11 \hat{j} + 7 \hat{k}] \Rightarrow \vec{F} = \sqrt{171} \times 10^{- 6} N$

$∴$ $α = 171$

Solution

Q.
$1 μ C$ charge moving with velocity $\vec{v} = (\hat{i} - 2 \hat{j} + 3 \hat{k}) m/s$ in the region of magnetic field $\vec{B} = (2 \hat{i} + 3 \hat{j} - 5 \hat{k}) T .$ The magnitude of force acting on it is $\sqrt{α} \times 10^{- 6} N$ . The value of $α$ is ________. [2026]

Ans.
(171)

$\vec{F} = q (\vec{v} \times \vec{B}) = 1 \times 10^{- 6}$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 2 & 3 \\ 2 & 3 & - 5 \end{matrix} |$

$\vec{F} = 10^{- 6} [\hat{i} + 11 \hat{j} + 7 \hat{k}] \Rightarrow \vec{F} = \sqrt{171} \times 10^{- 6} N$

$∴$ $α = 171$

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Solution

Q. 1 μC charge moving with velocity v→=(i^-2j^+3k^) m/s in the region of magnetic field B→=(2i^+3j^-5k^) T. The magnitude of force acting on it is α×10-6 N. The value of α is ________. [2026]

Ans. (171) F→=q(v→×B→)=1×10-6|i^j^k^1-2323-5| F→=10-6[i^+11j^+7k^]⇒F→=171×10-6 N ∴ α=171

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Q.
$1 μ C$ charge moving with velocity $\vec{v} = (\hat{i} - 2 \hat{j} + 3 \hat{k}) m/s$ in the region of magnetic field $\vec{B} = (2 \hat{i} + 3 \hat{j} - 5 \hat{k}) T .$ The magnitude of force acting on it is $\sqrt{α} \times 10^{- 6} N$ . The value of $α$ is ________. [2026]

Ans.
(171)

$\vec{F} = q (\vec{v} \times \vec{B}) = 1 \times 10^{- 6}$ $| \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 2 & 3 \\ 2 & 3 & - 5 \end{matrix} |$

$\vec{F} = 10^{- 6} [\hat{i} + 11 \hat{j} + 7 \hat{k}] \Rightarrow \vec{F} = \sqrt{171} \times 10^{- 6} N$

$∴$ $α = 171$