એક વિજભારિત કણ (\(m\) દળ અને \(q\) વિજભાર) \(X\) અક્ષ દિશામાં \(V _{0}\) વેગથી ગતિ કરે છે.જ્યારે તે ઉગમબિંદુ પાસેથી પસાર થાય ત્યારે તે \(\overrightarrow{ E }=- E \hat{ j }\) જેટલા એકસમાન વિદ્યુતક્ષેત્રમાં (જે \(x = d\) સુધી પ્રવર્તે છે) દાખલ થાય છે. \(x > d\) ક્ષેત્રમાં ઇલેક્ટ્રોનના ગતિપથનું સમીકરણ શું હશે?

A \(y=\frac{q E d}{m V_{0}^{2}}\left(\frac{d}{2}-x\right)\)
B \(y=\frac{q E d}{m V_{0}^{2}}(x-d)\)
C \(y =\frac{ qEd }{ mV _{0}^{2}} x\)
D \(y =\frac{ qEd ^{2}}{ mV _{0}^{2}} x\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(y=\frac{q E d}{m V_{0}^{2}}\left(\frac{d}{2}-x\right)\)

Step-by-step Solution

Detailed explanation

Let particle have charge \(q\) and mass \({ }^{\prime} m ^{\prime}\) Solve for \((q,m)\) mathematically \(F _{ x }=0, a _{ x }=0,( v )_{ x }=\) constant time taken to reach at \(P ^{\prime}=\frac{ d }{ V _{0}}= t _{0}( let )\)\(\ldots(1)\) (Along…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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