The magnetic field inside a solenoid is given by:
\[ B = \mu_0 n i, \]
where:
- \( B = 6.28 \times 10^{-3} \, \text{T} \) is the magnetic field,
- \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) is the permeability of free space,
- \( n = \frac{m}{\ell} \) is the number of turns per unit length,
- \( i = 5 \, \text{A} \) is the current,
- \( \ell = 0.5 \, \text{m} \) is the length of the solenoid.
Step 1: Rearranging the Formula
Substituting the given values:
\[ \mu_0 \left( \frac{m}{\ell} \right) i = B. \]
Rearranging to find \( m \):
\[ m = \frac{B \ell}{\mu_0 i}. \]
Step 2: Substituting the Values
Substituting the given values:
\[ m = \frac{6.28 \times 10^{-3} \times 0.5}{4\pi \times 10^{-7} \times 5}. \]
Simplifying:
\[ m = \frac{6.28 \times 10^{-3} \times 0.5}{12.56 \times 10^{-7}}. \]
Further simplification:
\[ m = \frac{3.14 \times 10^{-3}}{12.56 \times 10^{-7}}. \]
Calculating:
\[ m = 500. \]
Therefore, the value of \( m \) is 500.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below:
As shown in the diagram, an electron enters perpendicularly into a magnetic field. Using Fleming’s Left-Hand Rule, determine the direction of the force experienced by the electron.