Q.44 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 44 Solution

Topic: Moving Charges and Magnetism · Official NTA Booklet Code M1

Question

In the product F = q(v × B) = q v × (B î + B ĵ + B₀ k̂). For q = 1 and v = 2î + 4ĵ + 6k̂ and F = 4î − 20ĵ + 12k̂, what will be the complete expression for B?

✓

Verified Against NTA Final Answer Key

Option (2) : -6i - 6j - 8k

📚 Moving Charges and Magnetism Medium

📋 Given Parameters & Problem Setup

Charge (q) 1 C

Velocity Vector (v) 2 i + 4 j + 6 k

Magnetic Field Form B i + B j + B_0 k

Force Vector (F) 4 i - 20 j + 12 k

⚡

The 30-Second Exam Hall Shortcut: ⚡ k-Component Inspection: (v × B)_z = 2B - 4B = -2B = 12 $\implies$ B = -6

⏱️ Save ~25 seconds

Inspect the $\hat{k}$ component of $\vec{v} \times \vec{B}$ : $(v_x B_y - v_y B_x) = (2)(B) - (4)(B) = -2B$ . Since $F_z = 12$ , we immediately get $-2B = 12 \implies B = -6$ ! So $\vec{B}$ must begin with $-6\hat{i} - 6\hat{j}$ . Only Option (2) has $-6\hat{i} - 6\hat{j}$ ! Instant 10-second inspection matching Option (2)!

1 Compute the

\hat{k}

component of

\vec{v} \times \vec{B}

v_x B_y - v_y B_x = 2(B) - 4(B) = -2B

2 Equate to

F_z = 12

-2B = 12 \implies B = -6

3 Since the field has form

\vec{B} = B\hat{i} + B\hat{j} + B_0\hat{k}

, the first two coefficients are both

-6

4 Look at the options: Only Option (2) has

-6\hat{i} - 6\hat{j} - 8\hat{k}

5 Match Option (2).

🛡️

Why You Can 100% Trust This Shortcut: Canonical vector cross product component evaluation.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Formulating the Magnetic Force Cross Product

For charge $q = 1$ , the magnetic force is $\vec{F} = \vec{v} \times \vec{B}$ . Given $\vec{v} = 2\hat{i} + 4\hat{j} + 6\hat{k}$ and $\vec{B} = B\hat{i} + B\hat{j} + B_0\hat{k}$ :

\vec{v} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 4 & 6 \\ B & B & B_0 \end{vmatrix}

Step 2

Expanding the Determinant

Expand along the top row:

\vec{v} \times \vec{B} = \hat{i}(4 B_0 - 6 B) - \hat{j}(2 B_0 - 6 B) + \hat{k}(2 B - 4 B) = (4 B_0 - 6 B)\hat{i} - (2 B_0 - 6 B)\hat{j} - 2 B \hat{k}

Step 3

Comparing Components with the Given Force Vector

We are given $\vec{F} = 4\hat{i} - 20\hat{j} + 12\hat{k}$ : 1. From the $\hat{k}$ -component: $-2B = 12 \implies B = -6$ 2. From the $\hat{i}$ -component: $4 B_0 - 6 B = 4 \implies 4 B_0 - 6(-6) = 4 \implies 4 B_0 + 36 = 4 \implies 4 B_0 = -32 \implies B_0 = -8$ 3. Verify the $\hat{j}$ -component: $ $-(2 B_0 - 6 B) = -[2(-8) - 6(-6)] = -[-16 + 36] = -20 \quad (\text{Matches } F_y = -20)$

Step 4

Assembling the Magnetic Field Vector

Substitute $B = -6$ and $B_0 = -8$ into $\vec{B} = B\hat{i} + B\hat{j} + B_0\hat{k}$ :

\vec{B} = -6\hat{i} - 6\hat{j} - 8\hat{k}

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 1

✗ Incorrect

Verdict & Scientific Reason:

Swaps $B$ and $B_0$ ( $B = -8, B_0 = -6$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Swapping coordinates in vector cross product.

2 2

✓ 100% Correct

Verdict & Scientific Reason:

Exact vector components: $B = -6$ and $B_0 = -8$ , yielding $-6\hat{i} - 6\hat{j} - 8\hat{k}$ .

💡

Why this is airtight: None; rigorous vector determinant solution.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Sign error on $B$ and swapped indices.

⚠️

Student Fallacy (Why candidates pick this trap): Sign inversion error.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Sign error on $B$ ( $+6$ instead of $-6$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Flipping the sign of

-2B = 12

⚠️

NTA Trap Alert: k-Component Sign Trap

The $\hat{k}$ component is $(2B - 4B) = -2B$ . Setting $-2B = 12$ requires $B = -6$ . Students who mistakenly drop the minus sign write $2B = 12 \implies B = +6$ , falling for Option (4).

🛡️ How to avoid the -1 mark: Watch the order:

v_x B_y - v_y B_x = 2(B) - 4(B) = -2B

📖

Core NEET Syllabus Standard

NCERT Physics · Moving Charges and Magnetism Standard Benchmark

Core Scientific Principle Tested:

"The magnetic force is given by the cross product $\vec{F} = q(\vec{v} \times \vec{B})$ , solved component-wise using vector determinant methods."

Syllabus Focus: Magnetic Force and Vector Cross Products

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 44 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ k-Component Inspection: (v × B)_z = 2B - 4B = -2B = 12 ⟹ \implies⟹ B = -6

Step-by-Step Rigorous Workflow & Mathematical Proof

Formulating the Magnetic Force Cross Product

Expanding the Determinant

Comparing Components with the Given Force Vector

Assembling the Magnetic Field Vector

360° Option Elimination Engine Key Feature

NTA Trap Alert: k-Component Sign Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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Solve 4 NEET Questions a Day — One per Subject

The 30-Second Exam Hall Shortcut: ⚡ k-Component Inspection: (v × B)_z = 2B - 4B = -2B = 12 $\implies$ B = -6