Circulation of Magnetic Field

Q. Two wires with currents $2\text{A}$ and $I\text{A}$ are enclosed in a circular loop. Another wire with current $3\text{A}$ is situated outside the loop as shown.
The $\oint \overrightarrow{B}.d\overrightarrow{l}$ around the loop is


​​​​​​​$[$1 Mark$]$

1. ${\mu }_0$
2. $3{\mu }_0$
3. $6{\mu }_0$
4. $2{\mu }_0$

Q. A current I flows along the length of an infinitely long, straight and thin-walled pipe. Choose the correct option?

1. The magnetic field is different at different points inside the pipe
2. The magnetic field at any point inside the pipe is zero
3. The magnetic field is zero only on the axis of the pipe
4. The magnetic field at all points inside the pipe is the same but not zero

Q. 4.The electric field strength on the axis of cylinder at a point P, whose distance from the nearer face of the cylinder is r, is

Q. A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius $R_1$ and the outer conductor is hollow of inner radius $R_2$ and outer radius $R_3$. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as

Q. A charge of Q coloumb is located at the centre of a cube. If the centre is taken as the origin, then the flux coming out from the faces of the cube in the direction of X-axis will b

Q.

How many critical fields are in a hard superconductor?

Q.

What causes Earths electric field?

Q. A current of $\frac{1}{4\pi }$ amp is flowing in a long straight conductor. The line integral of magnetic induction around a closed path enclosing the current carrying conductor is

1. ${10}^{-7}wb/m$
2. $4\pi \times {10}^{-7}wb/m$
3. $16{\pi }^2\times {10}^{-7}wb/m$
4. $Zero$

Q.

A solid metallic cylinder carries a direct current. The magnetic field produced by it exists

1. Outside the cylinder only

2. Inside the cylinder only

3. Neither inside nor outside the cylinder

4. Both inside and outside the cylinder

Q.

A current of I ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius r. The magnetic field at any point outside the cylinder at a distance x form the axis is

1. 
   

2. 
   

3. 
   

4. 
   

Q. Two insulated rings, one of slightly smaller diameter than the other are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady current is set up in each of them

1. The two rings rotate into a common plane
2. The inner ring oscillates about its initial position
3. The inner ring stays stationary while the outer one moves into the plane of the inner ring
4. The outer ring stays stationary while the inner one moves into the plane of the outer ring

Q. The given diagram is a cross-sectional view of coaxial cable. The central conductor is surrounded by a rubber layer, which is surrounded by an outer conductor, which is further surrounded by another rubber layer. Current in the inner conductor is $1\text{A}$ directed out of the page, and current in the outer conductor is $3\text{A}$ into the page. The ratio of magnitude of magnetic field at point $\text{a}$ to that at point $\text{b}$ will be -

1. $1$
2. $2$
3. $1.5$
4. $2.5$

Q.

A closed-loop carrying current I lies in the x-z plane. The loop will experience a force if it is placed in a region occupied by a uniform magnetic field along.

1. x-axis

2. y-axis

3. z-axis

4. none of these

Q. Two large metal sheets carry surface currents as shown in figure. The current through a strip of width $dl$ is $Kdl$, where $K$ is a constant. The magnetic field at point $\text{Q}$ will be

1. ${\mu }_{0}K$
2. $\frac{{\mu }_{0}K}{2}$
3. zero
4. $2{\mu }_{0}K$

Q. A current $i\text{ampere}$ flows along an infinitely long straight thin walled tube of radius $R$, then the magnetic induction at any point inside the tube is

1. $\infty$
2. zero
3. $\frac{2i}{R}\text{T}$
4. $\frac{{\mu }_0}{4\pi }\frac{2i}{R}\text{T}$

Q.

A solid metallic cylinder carries a direct current. The magnetic field produced by it exists

1. Outside the cylinder only

2. Inside the cylinder only

3. Both inside and outside the cylinder

4. Neither inside nor outside the cylinder

Q. A rod, when suspended in a magnetic field, stays in the east-west direction. Can we be sure that the field is in the east-west direction? Can it be in the north-south direction?

Q. While talking about direction of current, dot symbol represents current coming out of a plane while a cross symbol represents current going into the plane.

1. False
2. True

Q. A thin straight conductor lies along the axis of a hollow conductor of radius $R=0.2\text{m}$, both of them carries $2\text{A}$ current in the same direction. Find magnetic induction at a distance $R$ from the axis of the hollow cylinder.

1. $20\times {10}^{-7}\text{T}$
2. $10\times {10}^{-7}\text{T}$
3. $30\times {10}^{-7}\text{T}$
4. $40\times {10}^{-7}\text{T}$

Q. The magnetic moment of the assumed dipole at the earth's centre is 8.0 × 10²² A m². Calculate the magnetic field B at the geomagnetic poles of the earth. Radius of the earth is 6400 km.

Q. A current of $I$ ampere flows along an infinitely long straight thin walled hollow metallic cylinder of radius $r.$ The magnetic field at any point inside the cylinder at a distance $x$ from the axis of the cylinder is

1. $\infty$
2. $\frac{{\mu }_{0}I}{2\pi r}$
3. $\text{zero}$
4. $\frac{{\mu }_{0}I}{2\pi x}$

Q. A coaxial cable consists of a thin inner conductor fixed along the axis of a hollow outer conductor. The two conductors carry equal currents in opposite directions. Let $B_1$ and $B_2$ be the magnetic fields in the region between the conductors and outside the hollow conductor respectively. Then:

1. $B_1\ne 0,B_2\ne 0$
2. $B_1=B_2=0$
3. $B_1\ne 0,B_2=0$
4. $B_1=0,B_2\ne 0$

Q. A magnetic dipole of magnetic moment $0.72\sqrt{2}\mathrm{A}{\mathrm{m}}^2$ is placed horizontally with the north pole pointing towards east. Find the position of the neutral point if the horizontal component of the earth's magnetic field is 18 μT.

Q. If long hollow copper pipe carries a direct current, the magnetic field associated with the current will be:

1. only outside the pipe
2. only inside the pipe
3. neither inside nor outside the pipe
4. both inside and outside the pipe

Q. A cylindrical wire of radius R carries a current directed out of the page as shown below. The current has a cross-sectional area density J that varies with distance r from the wire's axis according to the function $J=\frac{C}{r}$.
According to Ampere's Law, the current creates magnetic field both within the wire and outside the wire.
What current is enclosed in a circular loop that is centered on the wire's axis and has a radius $r<R$?

1. $2\pi Cr$
2. $\frac{C{r}^2}{2}$
3. $Cr$
4. $4Cr$
5. $2C$

Q. A steady current $I$ flows down a hollow cylindrical tube of radius a and is uniformly distributed around the tube. Let $r$ be the distance from the axis of symmetry of the tube to a given point. What is the magnitude of the magnetic field$B,$ at a point inside the tube?

1. $zero$
2. $\frac{2I}{rc}$
3. $\frac{4\pi (r-a)I}{r^2}$
4. $\frac{2Ir}{a^{2}c}$

Q. A long, straight, hollow conductor (tube) carrying a current has two sections E and C of unequal cross-sections joined by a conical section B. 1, 2 and 3 are points on a line parallel to the axis of the conductor. The magnetic fields at 1, 2 and 3 have magnitudes $B_1,B_2$ and $B_3$ :

1. $B_1<B_2<B_3$
2. $B_2$ cannot be found unless the dimensions of the section B are known
3. $B_1=B_2=B_3$
4. $B_1=B_2\ne B_3$

Q. A magnetic dipole of magnetic moment 0.72 A m² is placed horizontally with the north pole pointing towards south. Find the position of the neutral point if the horizontal component of the earth's magnetic field is 18 μT.

Q. If the earth's magnetic field has a magnitude 3.4 × 10⁻⁵ T at the magnetic equator of the earth, what would be its value at the earth's geomagnetic poles?

Q. The magnetic field at a point on the axis of a straight current-carrying conductor is _________.

1. Maximum
2. Minimum
3. Zero
4. $\frac{3dlsin\theta }{r^2}$