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(a) A circular coil of 30 turns and radius \(8.0 \mathrm{~cm}\) carrying a current of \(6.0 \mathrm{~A}\) is suspended vertically in a uniform horizontal magnetic field of magnitude \(1.0 \mathrm{~T}\). The field lines make an angle of \(60^{\circ}\)

Short Answer

Expert verified
The magnetic force acting on the coil in the magnetic field is \(F = 12.42 \, N\).

Step by step solution

01

Identify Known Quantities

From the problem, the known quantities are: number of turns, \(n = 30\), coil radius, \(a = 8.0 \, cm = 0.08 \, m\), current, \(I = 6.0 \, A\), magnetic field, \(B = 1.0 \, T\), and angle between coil and field lines, \(\theta = 60^\circ = \pi /3 \, rad\).
02

Calculate the Magnetic Force

We can use the formula for the magnetic force acting on a coil to calculate the force: \(F = n \cdot I \cdot B \cdot a \cdot sin(\theta)\). We substitute the given values into the formula to calculate the force: \(F = 30 \cdot 6.0 \cdot 1.0 \cdot 0.08 \cdot sin(\pi /3)\).
03

Simplifying

After substituting all the values the expression becomes \(F = 30 \cdot 6.0 \cdot 1.0 \cdot 0.08 \cdot 0.866\).
04

Solve for F

The multiplication of all the values gives the final answer, the force acting on the coil in the magnetic field.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Circular Coil
A circular coil, also known as a loop of wire, is an essential component in electromagnetism. It is simply a wire wound into a coil in a circular shape. The coil's shape affects the magnetic properties, influencing how it interacts with magnetic fields.

When a current flows through the coil, it generates its own magnetic field due to the movement of electric charge. This magnetic field behaves just like a dipole, with a north and south pole, and it adds to or reduces any external magnetic fields depending on their orientation.

Circular coils are used in many applications, such as transformers, motors, and inductors, due to their ability to efficiently produce and respond to magnetic fields.
Magnetic Field
A magnetic field describes the area around a magnet within which magnetic forces can be observed. It is an invisible field that permeates space and affects magnetic objects in its vicinity. Represented by field lines, the strength of a magnetic field is measured in teslas (T).

Magnetic fields can come from permanent magnets, like the ones used in compasses, or they can be created by moving electric charges, such as the current flowing through a wire.
  • The direction of a magnetic field is defined by the direction a north pole would move if placed in the field.
  • The field is strongest near the poles of a magnet and decreases in strength with distance.


In the exercise you're working on, the magnetic field is uniform across the area where the circular coil is placed.
Current
Current, in the context of electricity and magnetism, refers to the flow of electric charge through a conductor. It is measured in amperes (A), which indicates how much charge moves past a point in the circuit over one second.

The flow of current through a circular coil generates a magnetic field around the coil. This field's intensity is directly proportional to the amount of current flowing.
  • In the given exercise, the current is consistent at 6.0 A, ensuring a steady magnetic field is produced.
  • The direction of the current affects the direction of the induced magnetic field, following the right-hand rule.

It's crucial for students to grasp the concept of current, as it forms the backbone of much of electromagnetism and circuit theory.
Number of Turns
The number of turns in a coil significantly affects the magnetic properties of the coil. Each turn, or loop, of the wire contributes to the total magnetic field produced when an electric current passes through the coil.

More turns equate to a stronger magnetic field, given the same current. This is because each loop of current adds to the overall field strength.
  • In the exercise, the coil has 30 turns, which helps enhance the magnetic effects when combined with the current.
  • Careful consideration of the number of turns is essential in designing devices like inductors or transformers for desired magnetic characteristics.

The concept of "number of turns" is fundamental in understanding the relationship between electric currents and magnetic fields in inductive components.

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Most popular questions from this chapter

In Exercise \(4.11\) obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

A galvanometer coil has a resistance of \(12 \Omega\) and the metre shows full scale deflection for a current of \(3 \mathrm{~mA}\). How will you convert the metre into a voltmeter of range 0 to \(18 \mathrm{~V} ?\)

A closely wound solenoid \(80 \mathrm{~cm}\) long has 5 layers of windings of 400 turns each. The diameter of the solenoid is \(1.8 \mathrm{~cm} .\) If the current carried is \(8.0 \mathrm{~A}\), estimate the magnitude of \(\mathbf{B}\) inside the solenoid near its centre.

A uniform magnetic field of \(1.5\) ' exists in a cylindrical region of radius \(10.0 \mathrm{~cm}\), its direction parallel to the axis along east to west. A wire carrying current of \(7.0 \mathrm{~A}\) in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if, (a) the wire intersects the axis, (b) the wire is turned from N-S to northeast-northwest direction, (c) the wire in the N-S direction is lowered from the axis by a distance of \(6.0 \mathrm{~cm} ?\)

Two moving coil meters, \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have the following particulars: \(R_{1}=10 \Omega, N_{1}=30\) \(A_{1}=3.6 \times 10^{-3} \mathrm{~m}^{2}, B_{1}=0.25 \mathrm{~T}\) \(R_{2}=14 \Omega, N_{2}=42\), \(A_{2}=1.8 \times 10^{-3} \mathrm{~m}^{2}, B_{2}=0.50 \mathrm{~T}\) (The spring constants are identical for the two meters). Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of \(\mathrm{M}_{2}\) and \(\mathrm{M}_{1}\).

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