Question

For the mag. field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be (a) $0^{\circ}$ (b) $90^{\circ}$ (c) $180^{\circ}$ (d) $45^{\circ}$

Name: Problem 1889, Chapter 13: JEE Physics
Uploaded: 2021-10-02T09:24:11-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: For the mag. field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be (a) 0^∘ (b) 90^∘ (c) 180^∘ (d) 45^∘

   For the mag. field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be
(a) $0^{\circ}$
(b) $90^{\circ}$
(c) $180^{\circ}$
(d) $45^{\circ}$

JEE Physics

StemEZ 1st Edition

Chapter 13, Problem 1889

Instant Answer

Solved by Expert Narayan Hari

10/02/2021

Step 1

Step 1: The magnetic field due to a small current element is given by the Biot-Savart law, which states that the differential magnetic field dB at a point due to a differential current element idl is given by: \[dB = \frac{{\mu_0}}{{4\pi}} \frac{{idl \times Show more…

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For the mag. field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be (a) $0^{\circ}$ (b) $90^{\circ}$ (c) $180^{\circ}$ (d) $45^{\circ}$

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Key Concepts

Angle Dependence in Magnetic Field Generation

The dependence on the sine of the angle means that the contribution of a current element to the magnetic field is maximized when the angle between the element and the line joining it to the observation point is 90 degrees. In this configuration, the sine function reaches its maximum value of 1, which results in the greatest magnetic field for a given current element.

Biot-Savart Law

The Biot-Savart law describes how current elements produce magnetic fields. It states that the magnitude of the magnetic field contribution from a small segment of current is proportional to the current magnitude, the length of the segment, and the sine of the angle between the current direction and the line joining the segment to the observation point, while also decreasing with the square of the distance. This fundamental law is used to analyze the magnetic effects of various current configurations.

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