Question

In a solenoid in which the wires are wound such that each loop touches the adjacent ones, which of the following will increase the magnetic field inside the magnet? a) making the radius of the loops smaller b) increasing the radius of the wire c) increasing the radius of the solenoid d) decreasing the radius of the wire e) immersion of the solenoid in gasoline

Short answer

Answer: Decreasing the radius of the wire.

Step-by-step solution

Analyze option (a)

Making the radius of the loops smaller will not increase the number of turns per unit length or the current flowing through the wire. Therefore, this option will not increase the magnetic field inside the magnet.

Analyze option (b)

Increasing the radius of the wire will increase the resistance of the wire (R = ρ * (L/A), where ρ is the resistivity, A is the cross-sectional area). This will decrease the current flowing through the wire, which will not increase the magnetic field inside the magnet.

Analyze option (c)

Increasing the radius of the solenoid will not change the number of turns per unit length or the current flowing through the wire. Thus, this option will not increase the magnetic field inside the magnet.

Analyze option (d)

Decreasing the radius of the wire will decrease the resistance of the wire. This will increase the current flowing through the wire, which will increase the magnetic field inside the magnet. Therefore, option (d) is correct.

Analyze option (e)

Immersion of the solenoid in gasoline has no direct effect on the number of turns per unit length or the current flowing through the wire. Therefore, this option will not increase the magnetic field inside the magnet. In conclusion, the correct answer is option (d) - decreasing the radius of the wire will increase the magnetic field inside the magnet.

Key concepts

Magnetic Field

When talking about solenoids, the magnetic field is a crucial concept to consider. A solenoid is a coil of wire that, when electric current flows through it, generates a magnetic field. This field is strongest at the center of the coil and weakens as you move toward the ends. The strength of this magnetic field depends on several factors:

• The number of turns of wire in the solenoid. More turns mean a stronger field.
• The current passing through the wire. Higher current results in a stronger magnetic field.
• The length of the solenoid. A longer solenoid with the same number of turns will spread the magnetic field over a larger area, making it weaker per unit length.

To increase the magnetic field inside a solenoid, you should decrease the radius of the wire, which increases the current, or directly increase the current itself. This boosts the magnetic field without changing its shape.

Electric Current

Electric current is defined as the rate of flow of electric charge. In a solenoid coil, the electric current flows through the loops of wire, creating the magnetic field essential for many applications like electromagnets, inductors, and even some types of electric motors.

• The amount of current depends on the voltage applied and the resistance of the wire.
• Reducing the wire’s resistance leads to higher current flow for a given voltage.

In practical terms, decreasing the radius of the wire will reduce the resistance, thus allowing more current to flow for the same voltage. This increase in current results in a stronger magnetic field generated by the solenoid, as shown in our exercise solution.

Resistance

Resistance is a property of materials that opposes the flow of electric current. It is an important factor in determining how much current flows through a circuit. The resistance, denoted by the letter 'R', is calculated using the formula:\[ R = \rho \frac{L}{A} \]where:

• \( \rho \) is the resistivity of the material.
• \( L \) is the length of the wire.
• \( A \) is the cross-sectional area of the wire.

To reduce resistance, you can either reduce the resistivity, increase the cross-sectional area, or decrease the length. In the context of the solenoid problem, reducing the radius of the wire effectively reduces the resistance, resulting in increased current flow, which strengthens the magnetic field in the solenoid.

Physics Problems

Physics problems, like the one with the solenoid, require careful analysis of the situation and the interplay between different physical properties. Here are some tips for tackling physics problems:

• Identify what is being asked and list all the given information.
• Recognize the physics concepts that are applicable, such as magnetic fields, resistance, and current in this case.
• Carefully analyze how each factor (e.g., the radius of wires, number of coils) affects the desired outcome.
• Use relevant formulas to calculate and compare changes to these factors.
• Consider the real-world implications of the solution, like ensuring the safety and practicality of the configuration.

Developing a strong understanding of core concepts like the relationship between current and magnetic field, and the role of resistance, will build confidence in solving similar exercises effectively.