Dependence on Magnetic Field

Q. In the given figure the magnetix flux through the loop increases according to the relation ${\varphi }_B\left(t\right)=10t^2+20t$, where ${\varphi }_B$ is in milliwebers and $t$ is in seconds.
The magnitude of current through $R=2\Omega$ resistor at $t=5\text{s}$ is $\text{(in mA})$

Q. A circular loop of radius $r$ is moved away from a long current carrying wire, then induced current in the circular loop will be -

Assume the loop and wire are in the plane of paper of your notebook and the observer is observing from above the plane.

1. Clockwise
2. Anti-clockwise
3. No current will be induced
4. Initially clockwise, then anti-clockwise

Q.

A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

Q. A toroid having a rectangular cross-section $(a=2.00\text{cm}$ and $b=3.00\text{cm})$ and inner radius $r=4.00\text{cm}$ consists of $500$ turns of wire that carries a current $I=I_{max}\sin \omega t$ with $I_{max}=50.0\text{A}$ and a frequency $f=\frac{\omega }{2\pi }=60.0\text{Hz}.$ A coil that consists of $20$ turns of wire links with the toroid as shown in figure. Then which of the following is/are correct?

1. 
2. Maximum value of induced emf is $0.422V$
3. 
4. Maximum value of induced emf is $0.122V$

Q.

An infinitely long cylinder is kept parallel to an uniform magnetic field B directed along positive Z-axis. This direction of induced current as seen from the Z-axis will be

1. clockwise of the positive Z-axis

2. anti-clockwise of the positive Z-axis

3. zero

4. along the magnetic field

Q. find the locus of all the points where the resu†an t electric field vector will always have a bearing of 45 deg. with the axis of a short dipole

Q. What is the field of an electric dipole.for points on the axis and the points on the equatorial plane

Q. Two concentric circular coils having $10$ turns each are situated in the same plane. Their radii are $20\text{cm}$ and $40\text{cm}$ and they carry $0.2\text{A}$ and $0.3\text{A}$ current in opposite direction respectively. The magnetic field $\left(\text{in}{\text{Wb m}}^{-2}\right)$ at the centre is

1. $\frac{35}{4}{\mu }_0$
2. $\frac{{\mu }_0}{80}$
3. $\frac{7}{80}{\mu }_0$
4. $\frac{5}{4}{\mu }_0$

Q.

A hundred turns of insulated copper wire are wrapped around an iron cylinder of area ${10}^{-3}{m}^2$ and are connected to a resistor. The total resistance in the circuit is 10 ohms. If the longitudinal magnetic induction in the iron changes from 1 weber $m^{-2}$, in one direction to 1 Weber $m^{-2}$ in the opposite direction, how much charge flows through the circuit?

1. 2 x 10^–5 C
2. 2 x 10^–2 C
3. 2 x 10^–3 C
4. 2 x 10^–4 C

Q. The magnetic field in the cylindrical region shown in figure increases at a constant rate of 20 mT/sec. Each side of the square loop ABCD has a length of 1 cm and resistance of 16 ohm. Find the current in the wire AB if the switch S is closed

1. 1.25 X 10^-7 A , (anti-clockwise)
2. 1.25 X 10^-7 A , (clockwise)
3. 2.5 X 10^-7 A , (anti clockwise)
4. 2.5 X 10^-7 A , (clockwise)

Q. When a electric dipole placed along X axis find the locus of all those points on which electric field is perpendicular to electric dipole

Q. nta magnet is suspended in such a way that it oscillates in the horizontal plane. it makes 20 oscillations per minute at a place where dip angle is 30 degree and 15 oscillations per minute at a place where dip angle is 60 degree. ratio of the total earth, s magnetic field at the two places is?n

Q. A circular coil of area 8m2 and number of turns 20 is placed in a magnetic field of 2T with its plane perpendicular to it. It is rotated with an angular velocity of 20rev/s about its natural axis. The emf induced is ?

Q. A circular coil of mean radius $r$ and having $N$ turns is kept in a horizontal plane. A magnetic field $B$ exists in the vertical direction, as shown in the figure. In which of the following cases, an emf will be induced?

1. If the coil is held stationary and the magnetic field is non-uniform
2. If the coil is held stationary and the magnetic field is varying.
3. If the coil is rotated with an angular velocity $\omega$ about an axis passing through the centre and perpendicular to its plane and the magnetic field is uniform.
4. If the coil is rotated with an angular velocity $\omega$ about an axis passing through the diameter and the magnetic field is uniform.

Q. An infinitely long cylinder is kept parallel to a uniform magnetic field B directed along positive z axis. The direction of induced current as seen from the z axis will be

1. Along the magnetic field
2. Clockwise of the +ve z axis
3. Anticlockwise of the +ve z axis
4. Zero

Q. A long straight metal rod has a cavity of radius $a$ drilled parallel to the axis of the rod as shown in the figure. If the rod carries a current $i$ find the value of magnetic induction on the axis of the hole, [where $\text{OC}=c$]

1. $\frac{{\mu }_{0}ic}{\pi (b^2-a^2)}$
2. $\frac{{\mu }_{0}ic}{2\pi (b^2-a^2)}$
3. $\frac{{\mu }_{0}i(b^2-a^2)}{2\pi c}$
4. $\frac{{\mu }_{0}ic}{2\pi (a^2-b^2)}$

Q. The deflection in a moving coil galvanometer falls from $50$ divisions to $10$ divisions when a shunt of $12\Omega$ is connected with it. The resistance of galvanometer coil is ?

1. $48\Omega$
2. $12\Omega$
3. $24\Omega$
4. $36\Omega$

Q. A vertical rod of length l is moved with constant velocity v towards east. The vertical components of earth magnetic field is B and angle of dip is x. the induced e.m.f. in rod is 1) Blvsinx 2) Blvtanx 3) Blv cotx 4) Blv cosx

Q. 15.How to know about the direction of magnetic field

Q. A copper rod of length / is rotating about mid pointof rod, perpendicular to the magnetic field B withconstant angular velocity o. The induced emf between the two ends is .(1) 1/2B\overset⇀{ω l^2}(2) Bω l^2(3) 2Bω l^{}(4) Zero

Q.

A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

Q. An infinitely long cylinder is kept parallel to an uniform magnetic field B directed along positive z axis. The direction of induced current as seen from the z axis will be

1. clockwise of the +ve z axis
2. anticlockwise of the + ve z axis
3. zero
4. along the magnetic field

Q.

A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2.5 m east of the wire.

Q.

A long straight horizontal cable carries a current of 2.5 A in the direction 10º south of west to 10° north of east. The magnetic meridian of the place happens to be 10º west of the geographic meridian. The earth’s magnetic field at the location is 0.33 G, and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the cable). (At neutral points, magnetic field due to a current-carrying cable is equal and opposite to the horizontal component of earth’s magnetic field.)

Q. A metallic rod of 1 m length is rotated with a frequency of 50 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 m, about an axis passing through the centre and perpendicular to the plane of the ring (fig. 6.11). A constant and uniform magnetic field of 1 T parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?

Q.

Amagnetic needle free to rotate in a vertical plane parallel to themagnetic meridian has its north tip pointing down at 22º withthe horizontal. The horizontal component of the earth’smagnetic field at the place is known to be 0.35 G. Determine themagnitude of the earth’s magnetic field at the place.

Q. A circular loop of radius 4.0 cm is placed in a horizontal plane and carries an electric current of 5.0 A in the clockwise direction as seen from above. Find the magnetic field (a) at a point 3.0 cm above the centre of the loop (b) at a point 3.0 cm below the centre of the loop.

Q.

A hundred turns of insulated copper wire are wrapped around an iron cylinder of area ${10}^{-3}{m}^2$ and are connected to a resistor. The total resistance in the circuit is 10 ohms. If the longitudinal magnetic induction in the iron changes from 1 weber $m^{-2}$, in one direction to 1 Weber $m^{-2}$ in the opposite direction, how much charge flows through the circuit?

1. $2\times {10}^{-2}$C

2. $2\times {10}^{-3}$C

3. $2\times {10}^{-4}$C

4. $2\times {10}^{-5}$C

Q. The magnetic field in the cylindrical region shown in figure increases at a constant rate of 20 mT/sec. Each side of the square loop ABCD has a length of 1 cm and resistance of 16 ohm. Find the current in the wire AB if the switch S is closed

1. $1.25\times {10}^{-7}$A , (anti-clockwise)
2. $1.25\times {10}^{-7}$A , (clockwise)
3. $2.5\times {10}^{-7}$A , (anti clockwise)
4. $2.5\times {10}^{-7}$A , (clockwise)

Q. An infinitely long cylinder is kept parallel to a uniform magnetic field B directed along positive z axis. The direction of induced current as seen from the z axis will be

1. Clockwise of the +ve z axis
2. Anticlockwise of the +ve z axis
3. Zero
4. Along the magnetic field