CUET · PHYSICS · PYQ PAPER 2023

An electron enters a crossed electrical and magnetic field region with a speed of \( 100 \text{ m s}^{-1} \) along \( +x \)-axis and passes undeviated. The strength of magnetic field is 5.0 T and it acts along \( +z \)-axis. Give the electrical field in vector notations indicating its magnitude as well as direction :

A \( (500 \text{ V m}^{-1})\hat{j} \)
B \( -(500 \text{ V m}^{-1})\hat{k} \)
C \( (100 \text{ V m}^{-1})\hat{j} \)
D \( -(100 \text{ V m}^{-1})\hat{k} \)

Verified Solution

Answer & Solution

Correct Answer

(A) \( (500 \text{ V m}^{-1})\hat{j} \)

Step-by-step Solution

Detailed explanation

\( \vec{E} = -(\vec{v} \times \vec{B}) \) \( \vec{E} = -((100 \hat{i}) \times (5.0 \hat{k})) \) \( \vec{E} = -(500 (\hat{i} \times \hat{k})) \) \( \vec{E} = -(500 (-\hat{j})) \) \( \vec{E} = (500 \text{ V m}^{-1})\hat{j} \)

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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