Current answer is incorrect- please help, i\'ll rate highly! The picture shows a

Question

Current answer is incorrect- please help, i'll rate highly! The picture shows a cross-sectional view through three long straight current-carrying wires, which are each carrying current perpendicular to the page (or the screen). In this problem, use these values: the distance a = 30.0 cm; the current I = 6.50 amps. (a) Calculate the net force per unit length acting on the wire that carries a current of 3I out of the page, at x = +2a. Use a plus sign if the force is directed to the right, and a minus sign if the force is directed to the left.

Explanation / Answer

(a) According to the Biot-Savart-Laplace force law dF = i dl x B, the magnitude of the force per unit length (N m^-1) among two parallel wires separated by a distance d and carrying currents i1 and i2 is |F| = (mu0 i1 i2) / (2pi d). In our case, the force exterted by the wire at the origin is F_- = - mu0 3 I^2 / (2pi 2 a), while the force extered by the wire at x=-2a is F_+ = + (mu0 9 I^2) / (2pi 4 a). The signs are caused by the right-hand rule occurring in the Biot-Svart law: in the first case, both the currents are parallel, so that the wires attract each other, while in the other case they are opposite, so that they repel each other. The total force is F_tot = + (3/4) (mu0 I^2) / (2pi a). Now mu0 = 4pi 10^-7 N A^-2, so that mu0 / 2pi = 2 10^-7 N A^-2. Since I = 6.50 A and a = 30 cm = 3 10^-1 m, it is F_tot = 2 10^-5 N m^-1

(b) At x = +a, the total magnetic field is the (vectorial) su of the fields generated by all the three wires. According to the Biot-Savart law for the magnetic field dB =(mu0/4pi) i dl x r r^-3, the magnitude of the magnetic field induced by a wire carrying current i at a point at distance d from the wire is |B| = mu0 i / (2pi d) . The fields due to the wires at x = -2a and x = +a cancel out since their magnitudes are equal, but the directions are opposite. So, at x = + a there is only the magnetic field due to the wire at x = +2a which is directed downward: B = - mu0 3I / (2pi a) = - 1.3 10^-5 T (1 Tesla, symbol T, is equal to N A^-1 m^-1).

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.