A long solenoid is formed by winding 20 turns | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnetic field $B$ inside a long solenoid is given by the formula $B = \mu_0 n i$,where $n$ is the number of turns per unit length and $i$ is

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(A) The magnetic field $B$ inside a long solenoid is given by the formula $B = \mu_0 n i$,where $n$ is the number of turns per unit length and $i$ is the current.Given:$B = 20 	ext{ mT} = 20 	imes 10^{-3} 	ext{ T}$$n = 20 	ext{ turns/cm} = 20 	imes 100 	ext{ turns/m} = 2000 	ext{ turns/m}$$\frac{\mu_0}{4\pi} = 10^{-7} 	ext{ T m/A} \Rightarrow \mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m/A}$Rearranging the formula for current $i$:$i = \frac{B}{\mu_0 n}$Substituting the values:$i = \frac{20 	imes 10^{-3}}{4\pi 	imes 10^{-7} 	imes 2000}$$i = \frac{20 	imes 10^{-3}}{8\pi 	imes 10^{-4}}$$i = \frac{200}{8\pi} = \frac{25}{\pi} \approx \frac{25}{3.14} \approx 7.96 	ext{ A}$Rounding to the nearest integer,we get $i \approx 8 	ext{ A}$.

$A$ long solenoid is formed by winding $20$ $turns/cm$. The current necessary to produce a magnetic field of $20$ $mT$ inside the solenoid will be approximately ..... $A$ $(\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m/A})$.

Similar Questions

$A$ thin hollow copper pipe carries a direct current. Which of the following statements is incorrect?

Assertion : If the current in a solenoid is reversed in direction while keeping the same magnitude,the magnetic field energy stored in the solenoid decreases.
Reason : Magnetic field energy density is proportional to the square of the current.

$A$ solenoid of length $0.5\; m$ has a radius of $1\; cm$ and is made up of $500$ turns. It carries a current of $5\; A$. What is the magnitude of the magnetic field inside the solenoid?

$A$ long straight wire with a circular cross-section having radius $R$ is carrying a steady current $I$. The current $I$ is uniformly distributed across this cross-section. Then the variation of magnetic field due to current $I$ with distance $r$ $(r < R)$ from its centre will be:

$A$ direct current $I$ flows along the length of an infinitely long straight thin-walled pipe. Then the magnetic field is

Vedclass Test Series

Exam Paper Generator

Online Exam Module