Biot-Savart's Law Quiz

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In the equation for the magnetic induction dB, which variables represent the geometric relationship in the 3D space around the wire?

r and y (A) Signup and view all the answers

According to the content, how is the direction of the magnetic induction determined for a long straight wire?

Following the tangent to the concentric magnetic lines. (C) Signup and view all the answers

What is the form of the equation representing the magnetic induction dB at point P as per Biot-Savart's Law?

dB = -µ,I[.-(-!)] / (4nr) (B) Signup and view all the answers

Which statement about the substitution in the magnetic induction equation is true?

Using sin(θ) = F' + J is correct. (C) Signup and view all the answers

What is the nature of the magnetic field established by the Helmholtz coils?

Uniform magnetic field (B) Signup and view all the answers

At what point is the magnetic induction evaluated when using a current-carrying circular loop?

At the center of the loop (A) Signup and view all the answers

What is the significance of the term µ0 in the equation of magnetic induction?

It is a constant related to the magnetic permeability of free space. (A) Signup and view all the answers

Which rule is used to determine the direction of magnetic induction at the center of a circular loop?

Right hand thumb rule (D) Signup and view all the answers

What is the effect of increasing the current in the wire loop on the magnetic induction at its center?

It increases the magnetic induction (B) Signup and view all the answers

What is the distance from the center of the loop at which the magnetic induction needs to be calculated in the given scenario?

100 mm (D) Signup and view all the answers

What does the density of magnetic lines indicate in a region?

The magnitude of the magnetic field (D) Signup and view all the answers

Which of the following best describes Biot Savart's Law?

It describes the magnetic field generated by a current carrying wire (C) Signup and view all the answers

What effect does a variation in electric field have according to the content?

It induces a magnetic field (C) Signup and view all the answers

How is magnetic field intensity denoted and what is it analogous to?

It is denoted by 'B' and is analogous to electric field intensity 'E' (B) Signup and view all the answers

What observation did Danish scientist Oersted make?

The relationship between electric current and magnetic field (D) Signup and view all the answers

What do magnetic poles and charges have in common?

They both produce lines of force (C) Signup and view all the answers

What is the relationship between magnetic induction and the electric field?

Variation in electric field induces magnetic fields and vice versa (A) Signup and view all the answers

What role do magnetic forces play in relation to electric charges?

They produce attraction and repulsion like electric charges (C) Signup and view all the answers

What characterizes Helmholtz coils?

They consist of two coils positioned symmetrically on a common axis. (A) Signup and view all the answers

Which component of the magnetic induction at point P is canceled out?

dB cosθ, which is perpendicular to the axis. (B) Signup and view all the answers

According to Biot-Savart's law, how is the magnetic induction dB calculated?

$\mu_0 I d / (4 \pi \cdot (R' + x'))$ (C) Signup and view all the answers

What happens to the components of dB sinθ from all elements of the coil?

They add up in the same direction. (A) Signup and view all the answers

What is the effect of the arrangement of coils in Helmholtz coils on the magnetic field?

It produces a uniform magnetic field in the region between the coils. (C) Signup and view all the answers

What is meant by the term 'magnetic induction' at point P?

It describes the magnetic field strength experienced at that point. (C) Signup and view all the answers

Which term accurately describes the direction of the resultant magnetic induction at point P?

It aligns along the common axis of the coils. (D) Signup and view all the answers

What is the significance of integrating the expression for dB over the whole circumference of the coil?

It allows for the determination of total magnetic induction from all elements. (A) Signup and view all the answers

Study Notes

Biot-Savart's Law

This law describes the magnetic field created by a current-carrying wire.
The equation helps to calculate the strength of the magnetic field at a specific point around the wire.
It states that the magnetic induction (B) is proportional to the current (I), the length of the wire element (dl), and the sine of the angle between the wire element and the line joining the wire element to the point.

Magnetic Induction Due to a Long Straight Wire

The magnetic induction (B) around a long straight wire is calculated using a specific formula.
It is inversely proportional to the distance (r) from the wire and directly proportional to the current (I).
The direction of magnetic induction is determined by the right-hand thumb rule.

Magnetic Induction at the Center of a Circular Arc

The magnetic induction at the center of a circular arc carrying a current (I) is determined using Biot-Savart's Law.
It depends on the angle (θ) subtended by the arc at its center, the radius (R) of the arc, and the current (I).
The magnetic induction is directed inwards according to the right-hand thumb rule.

Helmholtz Coils

These coils are a setup of two identical circular coils placed at a distance equal to their radius.
The magnetic field at the center of the coils is uniform, creating a constant magnetic field in the region between the coils.
This setup is useful for experiments in physics labs where a uniform magnetic field is required.

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Description

Test your understanding of Biot-Savart's Law and its applications in calculating the magnetic field around current-carrying wires. This quiz covers magnetic induction due to long straight wires and circular arcs, emphasizing the right-hand thumb rule. Challenge your knowledge and see how well you grasp these concepts!