Three long parallel wires are 35 cm from one another Looking

Three long parallel wires are 3.5 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 8.00 A , but its direction in wire M is opposite to that in wires N and P (see the figure).

Part C

Determine the magnitude of magnetic force per unit length on wire N due to the other two.

Express your answer to two significant figures and include the appropriate units.

Part D

Determine the direction of magnetic force per unit length on wire N due to the other two.

Express your answer to two significant figures and include the appropriate units.

Part E

Determine the magnitude of magnetic force per unit length on wire P due to the other two.

Express your answer to two significant figures and include the appropriate units.

Part F

Determine the direction of magnetic force per unit length on wire P due to the other two.

Express your answer to two significant figures and include the appropriate units.

Solution

F_tot on M due to N and P

|F₂| / L = |F₃| / L = [mu_o I₁ I₂] / [2 (pi) r]

|F₂| / L = (2 * 10 ^-7 *8 * 8) / (0.035) N/m = 3.66 * 10^-4 N/m

F_tot on M points up, since the sideways components cancel

|F_tot| = 2 | F₂ | cos 30^o = 6.32 x 10^-4 N

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| F_tot | on N due to M and P

By symmetry, | F_tot | = 60^o

| F_tot | / L = (|F_tot|_y / L) sin(60^o) / L

| F_tot | / L = 3.66 * 10^-4 N/m

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similarly, the force on P is 60^o

| F_tot | / L = 3.66 * 10^-4 N/m