A particle having charge moving in plane in fields of and experiences a force of . The velocity of the particle at that instant is

Question

A particle having charge $10^{- 9} C$ moving in $x - y$ plane in fields of $0.4 \hat{j} N/C$ and $4 \times 10^{- 3} \hat{k} T$ experiences a force of $(4 \hat{i} + 2 \hat{j}) \times 10^{- 10} N$ . The velocity of the particle at that instant is ______ $m/s$ . [2026]

Smart Achievers · Accepted Answer

(1)

$\vec{F} = q \vec{E} + q (\vec{v} \times \vec{B})$

$(4 \hat{i} + 2 \hat{j}) \times 10^{- 10} = 10^{- 9} [0.4 \hat{j} + (v_{x} \hat{i} + v_{y} \hat{j}) \times (4 \times 10^{- 3}) \hat{k}]$

$(4 \hat{i} + 2 \hat{j}) \times 10^{- 10} = 10^{- 9} (0.4 \hat{j} - 4 \times 10^{- 3} v_{x} \hat{j} + 4 \times 10^{- 3} v_{y} \hat{i})$

$On comparing: v_{y} = 100, v_{x} = 50$

$\vec{v} = (50 \hat{i} + 100 \hat{j}) {ms}^{- 1}$

Solution

Q.
A particle having charge $10^{- 9} C$ moving in $x - y$ plane in fields of $0.4 \hat{j} N/C$ and $4 \times 10^{- 3} \hat{k} T$ experiences a force of $(4 \hat{i} + 2 \hat{j}) \times 10^{- 10} N$ . The velocity of the particle at that instant is ______ $m/s$ . [2026]

1 $50 \hat{i} + 100 \hat{j}$

2 $100 \hat{i} + 50 \hat{j}$

3 $- 50 \hat{i} + 100 \hat{j}$

4 $50 \hat{i} - 100 \hat{j}$

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Solution

Q. A particle having charge 10-9 C moving in x-y plane in fields of 0.4j^ N/C and 4×10-3k^ T experiences a force of (4i^+2j^)×10-10 N. The velocity of the particle at that instant is ______ m/s. [2026]

1 50i^+100j^

2 100i^+50j^

3 -50i^+100j^

4 50i^-100j^