A long straight wire on the z-axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point P, at the center of the loop, is 25 cm from the z-axis. An electron is projected from P with a velocity of 1.0 × 10⁶ m/s in the negative x-direction. What is the y component of the force on the electron? (e = 1.60 × 10^-19 C, μ₀ = 4π × 10^-7 T ∙ m/A) A) -1.0 × 10^-18 N B) +1.0 × 10^-18 N C) -2.0 × 10^-18 N D) +2.0 × 10^-18 N E) zero

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Quizplus · Accepted Answer

The force on the electron is given by the Lorentz force law: F = q(v x B), where q is the charge of the electron, v is its velocity, and B is the magnetic field. In this case, the magnetic field at point P is due to the current in the wire and is given by the Biot-Savart law: B = (μ0/4π)I(R^2 + z^2)^(-3/2)R, where I is the current in the wire, R is the radius of the loop, and z is the distance of the loop from the wire. Plugging in the given values, we find that B = 2.7 × 10^-5 T. Since the velocity of the electron is in the negative x-direction, the force on it will be in the positive y-direction (i.e., perpendicular to both the velocity and the magnetic field). Therefore, the y component of the force is given by Fy = qvB, which comes out to be -1.0 × 10^-18 N.

A Long Straight Wire on the Z-Axis Carries a Current