MCQ
A hollow cylinder having infinite length and carrying uniform current per unit length $\lambda$ along the circumference as shown. Magnetic field inside the cylinder is
- A$\frac{{{\mu _0}\lambda }}{2}$
- ✓$\mu_0 \lambda$
- C$2\mu_0 \lambda$
- Dnone
✓
Answer
Correct option: B.
$\mu_0 \lambda$
b
Hint: Apply Biot Savart's law
Hint: Apply Biot Savart's law
Step $1:$
Given a hollow cylinder that has infinite length and carrying current per unit length $\lambda$ along the circumference.
Here $\lambda=\frac{ I }{2 \pi r }$ ie.., current flowing per unit length.
$I =\lambda 2 \pi r \text { (1) }$
The magnetic field inside the cylinder is given by
$B =\frac{\mu_0}{4 \pi} \times \frac{2 I }{ r } \text { (2) }$
Step $2:$
Substitute the value of I from eq: $(1)$ in $(2)$ we get
$B =\frac{2 \mu_0}{4 \pi} \times \frac{\lambda 2 \pi r }{ r }$
$\Rightarrow B =\mu_0 \lambda$
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