Question

A current $$i$$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

A. $$\frac{{{\mu _0}}}{{4\pi }}.\frac{{2i}}{r}\,{\text{tesla}}$$
B. zero  
C. infinite
D. $$\frac{{2i}}{r}\,{\text{tesla}}$$
Answer :   zero
Solution :
Using Ampere’s law at a distance $$r$$ from axis, $$B$$ is same from symmetry.
$$\int {B.dl = {\mu _0}i\,\,\,\,\,\,{\text{i}}{\text{.e}}{\text{.,}}\,B \times 2\pi r = {\mu _0}i} $$
Here $$i$$ is zero, for $$r < R,$$  whereas $$R$$ is the radius
$$\therefore B = 0$$

Releted MCQ Question on
Electrostatics and Magnetism >> Magnetic Effect of Current

Releted Question 1

A conducting circular loop of radius $$r$$ carries a constant current $$i.$$ It is placed in a uniform magnetic field $${{\vec B}_0}$$ such that $${{\vec B}_0}$$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

A. $$ir\,{B_0}$$
B. $$2\pi \,ir\,{B_0}$$
C. zero
D. $$\pi \,ir\,{B_0}$$
View Answer
Releted Question 2

A battery is connected between two points $$A$$ and $$B$$ on the circumference of a uniform conducting ring of radius $$r$$ and resistance $$R.$$ One of the arcs $$AB$$  of the ring subtends an angle $$\theta $$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is

A. proportional to $$2\left( {{{180}^ \circ } - \theta } \right)$$
B. inversely proportional to $$r$$
C. zero, only if $$\theta = {180^ \circ }$$
D. zero for all values of $$\theta $$
View Answer
Releted Question 3

A proton, a deuteron and an $$\alpha - $$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $${r_p},{r_d},$$  and $${r_\alpha }$$ denote respectively the radii of the trajectories of these particles, then

A. $${r_\alpha } = {r_p} < {r_d}$$
B. $${r_\alpha } > {r_d} > {r_p}$$
C. $${r_\alpha } = {r_d} > {r_p}$$
D. $${r_p} = {r_d} = {r_\alpha }$$
View Answer
Releted Question 4

A circular loop of radius $$R,$$ carrying current $$I,$$ lies in $$x - y$$  plane with its centre at origin. The total magnetic flux through $$x - y$$  plane is

A. directly proportional to $$I$$
B. directly proportional to $$R$$
C. inversely proportional to $$R$$
D. zero
View Answer

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Magnetic Effect of Current

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