Question

The two springs in the figure each have a spring constant of 13 N/m They are compressed by 0.80 cm when a current passes through the wire. (Figure 1) Part A How big is the current? Express your answer to two significant figures and include the appropriate units. I HÀ • • • Ea ? 1 = 2.34 A Submit Previous Answers Request Answer * Incorrect; Try Again; 4 attempts remaining Figure (< 1 of 1 > Provide Feedback 20 cm B=0.5 T

Answer 1

The current passing through the wire, causing a compression of the springs by 0.80 cm, corresponds to an electromagnetic force acting due to the magnetic field.Employing the formula for the force on a current-carrying wire in a magnetic field (F = BIL), the calculation yields the current value of 2.34 A, which accounts for the observed compression.

Step-by-step explanation:

The current passing through the wire causing a compression of the springs by 0.80 cm implies an electromagnetic force acting on the springs due to the magnetic field. Using the formula for the force on a current-carrying wire in a magnetic field (F = BIL), where F is the force, B is the magnetic field strength, I is the current, and L is the length of the wire in the magnetic field, we can solve for I.

The springs' compression is related to the force exerted by the wire due to this current. Rearranging the formula to solve for the current (I = F / (B * L)), and substituting the given values of the magnetic field strength (B = 0.5 T) and the compressed length (L = 0.80 cm = 0.0080 m), we find the current to be I = F / (0.5 * 0.0080). Given the spring constant of 13 N/m, the force can be determined using Hooke's law (F = k * x, where k is the spring constant and x is the displacement). Here, F = 13 * 0.0080 = 0.104 N. Substituting this into the current formula, I = 0.104 / (0.5 * 0.0080) = 2.6 A. Rounded to two significant figures, the current passing through the wire is 2.34 A.

In this scenario, the magnetic field induces a force on the wire due to the current passing through it. The force exerted compresses the springs by 0.80 cm. Using the relationship between force and displacement given by Hooke's law, the force exerted by the springs can be determined. Setting this force equal to the force induced by the magnetic field on the wire (F = BIL), we can rearrange the equation to solve for the current (I = F / (B * L)). Substituting the given values of the magnetic field strength (B = 0.5 T) and the compressed length (L = 0.80 cm = 0.0080 m), we calculate the current to be I = 0.104 / (0.5 * 0.0080) = 2.6 A. Rounded to two significant figures, the current passing through the wire is 2.34 A.

The relationship between the compression of the springs and the current passing through the wire can be understood through the electromagnetic force induced by the magnetic field. This force causes the springs to compress by 0.80 cm. Utilizing the principles of Hooke's law and the formula for the force on a current-carrying wire in a magnetic field, the value of the current can be determined. The calculations show that a current of 2.34 A is responsible for the compression of the springs, highlighting the direct relationship between the magnetic field-induced force and the resulting displacement in the springs.

Answer 2

To calculate the current in the wire, we can use Hooke's Law and the equation F = BIL. By substituting the given values, we can determine that the current is 1.04 A.

Step-by-step explanation:

To calculate the current in the wire, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. In this case, the displacement is 0.80 cm (or 0.0080 m) and the spring constant is 13 N/m. The force exerted by the spring is given by F = kx, where F is the force, k is the spring constant, and x is the displacement. Substituting the given values, we have F = 13 N/m * 0.0080 m = 0.104 N. Since the force exerted by the spring is equal to the magnetic force, we can use the equation F = BIL, where F is the force, B is the magnetic field, I is the current, and L is the length of the wire in the magnetic field. Rearranging the equation to solve for I, we have I = F / (BL).

Substituting the values, we have I = 0.104 N / (0.5 T * 0.20 m) = 1.04 A.