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].

Question

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]., - e U B 0 2 2 i ^ - j ^, - e U B 0 2 i ^ - j ^, - e U B 0 2 i ^ - j ^, - e U B 0 i ^ - j ^

MARKS App · Accepted Answer

Magnetic field at origin due to wire at x = 1 cm is B 0 = μ 0 i 2 π 0 . 01 ⊙ Magnetic field at origin due to wire at x = - 2 cm is B = μ 0 i 2 π 0 . 02 ⊗ Therefore, the net magnetic field at origin will be, B → n e t = μ 0 i 2 π 0 . 02 ⊙ = B 0 2 k ^ The velocity of the electron is given as v → = U 2 i ^ + U 2 j ^ The force on the electron will be, F → = e v → × B → = e U 2 i ^ + U 2 j ^ × B 0 2 k ^ ⇒ F → = - e U B 0 2 2 i ^ - j ^

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