Q.48. A 1 C charge moving with velocity in the region of magnetic field . The magnitude of force ac

Q: What is the correct answer for this exam Physics Q48?

The correct answer is 171. Sol. The magnetic force on a moving charge is given by $\vec{F} = q(\vec{v} \times \vec{B})$. Given $q = 1 \mu C = 10^{-6} \text{ C}$. $\vec{v} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - 5\hat{k}$. $\vec{v} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & -2 & 3 \\ 2 & 3 & -5 \end{vmatrix} = \hat{i}((-2)(-5) - (3)(3)) - \hat{j}((1)(-5) - (3)(2)) + \hat

Q: Q.48. A 1 C charge moving with velocity in the region of magnetic field . The magnitude of force acting on it is . The value of is _______.

The correct answer is 171. Sol. The magnetic force on a moving charge is given by $\vec{F} = q(\vec{v} \times \vec{B})$. Given $q = 1 \mu C = 10^{-6} \text{ C}$. $\vec{v} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - 5\hat{k}$. $\vec{v} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & -2 & 3 \\ 2 & 3 & -5 \end{vmatrix} = \hat{i}((-2)(-5) - (3)(3)) - \hat{j}((1)(-5) - (3)(2)) + \hat

Question

Q.48. A 1 C charge moving with velocity  in the region of magnetic field . The magnitude of force acting on it is . The value of  is _______.

FirstInTest · Accepted Answer

Sol. The magnetic force on a moving charge is given by $\vec{F} = q(\vec{v} 	imes \vec{B})$. Given $q = 1 \mu C = 10^{-6} 	ext{ C}$. $\vec{v} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - 5\hat{k}$. $\vec{v} 	imes \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -2 & 3 \ 2 & 3 & -5 \end{vmatrix} = \hat{i}((-2)(-5) - (3)(3)) - \hat{j}((1)(-5) - (3)(2)) + \hat{k}((1)(3) - (-2)(2)) = \hat{i}(10 - 9) - \hat{j}(-5 - 6) + \hat{k}(3 + 4) = \hat{i} + 11\hat{j} + 7\hat{k}$. So $\vec{F} = 10^{-6} (\hat{i} + 11\hat{j} + 7\hat{k}) 	ext{ N}$. The magnitude of the force is $|\vec{F}| = 10^{-6} \sqrt{1^2 + 11^2 + 7^2} = 10^{-6} \sqrt{1 + 121 + 49} = 10^{-6} \sqrt{171} 	ext{ N}$. The problem states the magnitude of force is $\sqrt{\alpha} 	imes 10^{-6} 	ext{ N}$. Comparing, $\alpha = 171$.

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