AP EAMCET · PHYSICS · Magnetic Effects of Current

Two infinitely long wires each carrying the same current and pointing in $+ y$ direction are placed in the $x y$ - plane, at $x = - 2 cm$ and $x = 1 cm$ . An electron is fired with speed $U$ from the origin making an angle of $+ 45 °$ from the $x$ - axis. The force on the electron at the instant it is fired is
[ $B_{0}$ is the magnitude of the field at origin due to the wire at $x = 1 cm$ alone].

A $\frac{- e U B_{0}}{2 \sqrt{2}} (\hat{i} - \hat{j})$
B $\frac{- e U B_{0}}{2} (\hat{i} - \hat{j})$
C $\frac{- e U B_{0}}{\sqrt{2}} (\hat{i} - \hat{j})$
D $- e U B_{0} (\hat{i} - \hat{j})$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{- e U B_{0}}{2 \sqrt{2}} (\hat{i} - \hat{j})$

Step-by-step Solution

Detailed explanation

Magnetic field at origin due to wire at x=1 cm is B0=μ0i2π0.01⊙ Magnetic field at origin due to wire at x=-2 cm is B=μ0i2π0.02⊗ Therefore, the net magnetic field at origin will be, B→net=μ0i2π0.02⊙=B02 k^ The…

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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