A coil of mass m and charge q moves with a constant velocity v along the positive x−direction . It enters a region containing a uniform magnetic field B directed along the negative z−direction , extending from x=a→x=b. The minimum value of v required so that the paRTICLE CAN JUST ENTER THE REGION XB IS

Question

A coil of mass m and charge q moves with a constant velocity v along the positive x−direction . It enters a region containing a uniform magnetic field B directed along the negative z−direction , extending from x=a→x=b. The minimum value of v required so that the paRTICLE CAN JUST ENTER THE REGION X>B IS

Filo · Accepted Answer

Answer: CSolution: Let us consider a thickness

d x

of wire . Let it be at a distance

x

from the centre

O

Number of turns per unit length

= \frac{N}{b - a}

:. Number of turns in thickness

d x = \frac{N}{b - a} d x

Small amount of magnetic field is produced at

O

due to thickness

d x

of the wire .

d B = \frac{μ _{0}}{2} \frac{N I}{b - a} \frac{d x}{x}

On integrating , we get ,

B = \int_{a}^{b} \frac{μ _{0}}{2} \frac{N I}{b - a} \frac{d x}{x} = \frac{μ _{0}}{2} \frac{N I}{b - a}

\int_{a}^{b} \frac{d x}{x} = \frac{μ _{0}}{2} \frac{N I}{b - a} [lo g_{e} x]_{a}^{b}

B = \frac{μ _{0}}{2} \frac{N I}{b - a} \frac{lo g _{e} ( b )}{a}

Question Text	A coil of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x - d i r e c t i o n$ . It enters a region containing a uniform magnetic field $B$ directed along the negative $z - d i r e c t i o n$ , extending from $x = a \to x = b$ . The minimum value of $v$ required so that the paRTICLE CAN JUST ENTER THE REGION $X > B$ IS
Answer Type	Text solution:1
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