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# A Magnetic Field of 100 G (1 G = 10−4 T) is Required Which is Uniform in a Region of Linear Dimension About 10 cm and Area of Cross-section About 10^−3 m^2. - CBSE (Science) Class 12 - Physics

ConceptSolenoid and the Toroid - the Solenoid

#### Question

A magnetic field of 100 G (1 G = 10−4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10−3 m2. The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m−1. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic

#### Solution

Magnetic field strength, B = 100 G = 100 × 10−4 T

Number of turns per unit length, n = 1000 turns m−1

Current flowing in the coil, I = 15 A

Permeability of free space, mu_0=4pixx10^-7 TmA^-1

Magnetic field is given by the relation,

B=mu_0nI

therefore nI=B/mu_0

=(100xx10^-4)/(4pix10^-7)=7957.74

~~8000 A/m

If the length of the coil is taken as 50 cm, radius 4 cm, number of turns 400, and current 10 A, then these values are not unique for the given purpose. There is always a possibility of some adjustments with limits.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 4: Moving Charges and Magnetism
Q: 15 | Page no. 170

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Solution A Magnetic Field of 100 G (1 G = 10−4 T) is Required Which is Uniform in a Region of Linear Dimension About 10 cm and Area of Cross-section About 10^−3 m^2. Concept: Solenoid and the Toroid - the Solenoid.
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