Concept #1: Magnetic Force Between Parallel Currents

Practice: Two very long wires of unknown lengths are a parallel distance of 2 m from each other. If both wires have 3 A of current flowing through them in the same direction, what must the force per unit length on each wire be?

BONUS: Is the mutual force between the wires attractive or repulsive?

Two parallel, straight wires are 7.0 cm apart and each carries an 18.0 A current in the same direction. One wire is securely anchored, and the other is attached to a movable cart. If the force needed to move the wire when it is not attached to the cart is negligible, with what force does the wire pull the cart? Both wires are 50.0 m long. Note that the dyne is the unit of force in the cm, g, s system of units (often called the "cgs" system).
A) 9300 dynes
B) 370 dynes
C) 660 dynes
D) 4600 dynes

A long, straight wire carrying a 1.5 kA current is securely anchored at both ends. Another straight, 2m wire is anchored to a 15 kg block, with the two wires parallel and 5 cm apart. If the coefficient of static friction between the block and the ground is 0.5, what magnitude and direction of current needs to run through the second wire to get the block moving? If μk = 0.3, what would the acceleration of the block be once it started moving?

A loose spiral spring carrying no current is hung from a ceiling . When a switch is thrown so that a current exists in the spring, how do the coils move?
A) closer together
B) farther apart
C) not at all
D) widening the loop diameter

Two high-current transmission lines carry current of I1 = 1.23 A and I2 = 2.32 A in the same direction and are suspended parallel to each other with a separation of 0.560 m apart. The vertical posts supporting these wires divide then into straight 20.0 m long segments.
What is the magnetic force one segment exerts on another, direction and magnitude?

Two high-current transmission lines carry current of I1 = 1.23 A and I2 = 2.32 A in the same direction and are suspended parallel to each other with a separation of 0.560 m apart. The vertical posts supporting these wires divide then into straight 20.0 m long segments.
If the currents are running in opposite direction what is the force then, direction and magnitude?

In the figure below, the two long straight wires are separated by a distance of d = 0.40 m. The currents are I1 = 5.0 A to the right in the upper wire and I 2 = 6.0 A to the left in the lower wire. What is the magnitude and direction of the force on wire 2 due to wire 1 if the wire 1 is 10 cm long?

Two wires are separated by d and carry currents I1 and I2, respectively. However, we don't know yet the direction of the current I1 and I2. What we knnow is that the two wires repel each other. Which of the following false?
a. The direction of current I1 and I2 are opposite
b. Both F12 and F21 are inversely proportional to the square of the distance d
c. Always F12 = -F21 even if I1 is larger than I2
d. The magnitude of the magnetic field in the area between the two wires is stronger than those in the other regions
e. There is no point in the area between the two wires, where the magnetic field is zero

As shown in the figure, four long parallel wires lie on the corners of a square, with a 5th at the center. All wires carry identical currents, with directions shown in the figure (a cross inside a circle means the current is into the page while a dot inside a circle means the current is out of the page). What is the direction of the net force on the central wire (angles are measured from the +x axis)?
(1) 0°
(2) 45°
(3) 90°
(4) 135°
(5) 270°

Four parallel wires, a, b, c, d, are placed at the corners of a square glass beams as shown. (The insert shows the end view from the left). Wires a and c carry parallel currents to the right and wires b and d to the left. Study all possible interactions between the currents (six interactions altogether) and tell:
How many attractive interactions you find? _____
How many repulsive ones? _____

Two long straight parallel wires carry current in opposite directions, as shown in the sketch. The force that one wire exerts on the other is
A) repulsive
B) attractive
C) zero

A rectangular loop of wire (with sides labeled as 1, 2, 3, and 4) having width w = 3.00 cm and length l = 6.00 cm, carrying a current iloop = 25.0 A, is located at the distance d = 3.00 cm from a long, straight wire carrying a current i = 60.0 A. μ0 = 4π x 10-7 Tm/A.What is the net force on the rectangular loop? Show all the steps.

Two identical parallel sections of wire are connected parallel to a battery as shown. The two sections of wire are free to move. When the switch is closed, the wires
1. will accelerate towards each other.
2. will heat up, and remain motionless.
3. will accelerate away from each other.