Magnetic Field Due to a Straight Long Wire

Q.

When a long wire carrying a steady current is bent into a circular coil of one turn, the magnetic induction at its centre is B. When the same wire carrying the same current is bent to form a circular coil of n turns of a smaller radius, the magnetic induction at the centre will be

1. nB

2. $\frac{B}{n^2}$

3. $n^{2}B$

4. $\frac{B}{n}$

Q. Magnetic field at point P inside solenoid of n turns per unit length and current i is

1. ${\mu }_{0}ni$
2. $\frac{{\mu }_{0}ni}{\sqrt{2}}$
3. $\frac{{\mu }_{0}ni}{2}$
4. $\sqrt{2}{\mu }_{0}ni$

Q.

A copper wire of diameter 1.6 mm carries a current of 20 A. Find the maximum magnitude of the magnetic field $\overrightarrow{B}$ due to this current.

Q. Shown below is a semi-infinite wire carrying current I. What will be magnetic field at point P, which is d units away from one of its end?

1. $\frac{{\mu }_{0}I}{8\pi d}$
2. $\frac{{\mu }_{0}I}{d}$
3. $\frac{{\mu }_{0}I}{2\pi d}$
4. $\frac{{\mu }_{0}I}{4\pi d}$

Q.

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the sides of the loop. If a steady current I is established in the wire, as shown in Fig., the loop

1. rotate about an axis parallel to the wire

2. move towards the wire

3. move away from the wire

4. remain stationary.

Q.

The magnetic induction at a point P which is distant 4 cm from a long current carrying wire is ${10}^{-3}$ Telsa.The field of induction at a distance 12 cm from the same current would be

1. 
   

2. 
   

3. 
   

4. 
   

Q. Two infinitely long insulated wires are kept perpendicular to each other. They carry currents $I_1=2A$ and $I_2=1.5A$.
i) Find the magnitude and direction of the magnetic field at P.
ii) If the direction of current is reversed in one of the wires. What would be the magnitude of the field B?

1. $2\times {10}^{-5}T$, normally into the plane of the paper, $2\sqrt{2}\times {10}^{-5}T$
2. $2\times {10}^{-5}T$, normally out of the plane of the paper, $2\sqrt{2}\times {10}^{-5}T$
3. $2\times {10}^{-5}T$, normally into the plane of the paper, Zero
4. $2\times {10}^{-5}T$, normally into the plane of the paper, Zero

Q. Two very thin metallic wires placed along X– and Y–axes carry equal currents as shown in figure. AB and CD are lines at ${45}^{\circ }$ with the axes with origin of axes at O. The magnetic fields will be zero on the line

1. AB
2. CD
3. Segment OB only of line AB
4. Segment OC only of line CD

Q. A conducting rod $\text{PQ}$ of length $l=2\text{m}$ is moving at a speed of $2{\text{ms}}^{-1}$ making an angle of ${60}^{\circ }$ with its length. A uniform magnetic field $B=\sqrt{3}\text{T}$ exists in a direction perpendicular to the plane of motion. Then

1. $V_P-V_Q=4\text{V}$
2. $V_P-V_Q=6\text{V}$
3. $V_P-V_Q=8\text{V}$
4. $V_P-V_Q=10\text{V}$

Q.

The resistance of hot tungsten filament is about 10 times to that of cold tungsten filament. What will be the resistance of 100 W and 220 V lamp when not in use?

1. 4.84 ohm

2. 484 ohm

3. 48.4 ohm

4. 4840 ohm

Q.

What is the SNOW rule? Explain the purpose of the SNOW rule.

Q.

A magnetic compass shows a deflection when placed near a current-carrying wire. How will the deflection of the compass get affected if the current in the wire is increased? Support your answer with a reason.

Q. Work required to rotate given square frame by ${180}^{\circ }$ can be given as

1. $\frac{{\mu }_0}{2\pi }{i}_1{i}_{2}aln\left(2\right)$
2. $\frac{{\mu }_0}{\pi }{i}_1{i}_{2}aln\left(2\right)$
3. $\frac{{\mu }_0}{\pi }{i}_1{i}_{2}a$
4. $\frac{{\mu }_0}{2\pi }{i}_1{i}_{2}a$

Q.

A current of 10 A is established in a long wire along the positive z-axis . Find the magnetic field $\overrightarrow{B}$ at the point (1 m, 0, 0).

Q.

A wire ABCDEF (with each side of length L) bent as shown in Fig. and carrying a current I is placed in a uniform magnetic field B parallel to the positive y - direction. What is the magnitude and direction of the force experienced by the wire?

1. BIL along negative z-direction

2. BIL along positive z-direction

3. $\frac{B{I}^2}{L}$ along positive z-direction

4. $\frac{BL}{I}$ along negative z-direction

Q. What will be the resultant magnetic field at origin due to four infinitely long wires. If each wire produces magnetic field 'B' at origin

1. $4B$
   
2. $Zero$
3. $\sqrt{2}B$
   
4. $2\sqrt{2}B$

Q.

Which of the following graphs shows the variation of magnetic induction B with distance r from a long wire carrying current

[NCERT 1984; MNR 1998; MP PMT]

1. 
   

2. 
   

3. 
   

4. 
   

Q.

The strength of the magnetic field at a point r near a long straight current carrying wire is B. The field at a distance $\frac{r}{2}$ will be

[MP PMT 1990]

1. 2B

2. 4B

3. 
   

4. 
   

Q. An electric dipole consisting of two opposite charges of $2\times {10}^{-6}C$ each, separated by a distance of 3 cm is placed in an electric field of $2\times {10}^{5}N/C$. The maximum torque on the dipole will be

1. $12\times {10}^{-1}Nm$
2. $12\times {10}^{-3}Nm$
3. $24\times {10}^{-1}Nm$
4. $24\times {10}^{-3}Nm$

Q. A magnetic flux of $5.5\times {10}^{-4}\text{Wb}$ is linked with a coil of resistance $10\Omega$ and $1\text{turn}$. If the magnetic flux is changed to $5\times {10}^{-4}\text{Wb}$ in $0.1\text{sec}$, the induced charge in the coil is,

1. $50\mu \text{C}$
2. $5\mu \text{C}$
3. $2\mu \text{C}$
4. $20\mu \text{C}$

Q. Two very long straight parallel wires carry steady currents $i$ and $2i$ in opposite directions. The distance between the wires is $d$. At a certain instant of time, a point charge $q$ is at a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity whose magnitude is $v$ is perpendicular to this plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is

1. $\frac{{\mu }_{0}iqv}{2\pi d}$
2. $\frac{{\mu }_{0}iqv}{\pi d}$
3. $\frac{3{\mu }_{0}lqv}{2\pi d}$
4. Zero

Q. The magnetic field due to a short magnet, at a point on its axis, at a distance $X\text{cm}$ from the middle point of the magnet, is $200\text{Gauss}$. The magnetic field at a point on the equatorial axis, at a distance $X\text{cm}$ from the centre of magnet, will be

1. $100\text{Gauss}$
2. $400\text{Gauss}$
3. $50\text{Gauss}$
4. $200\text{Gauss}$

Q. A tangent galvanometer is connected directly to an ideal battery. If the number of turns in the coil is doubled, the deflection will

1. increase
2. decrease
3. remain unchanged
4. any of these

Q.

An electric current is flowing in a long straight wire. The magnetic field due to this current a distance of 5 cm from the wire is 10 T. The magnetic field at a distance of 10 cm from the wire is

1. 2.5 T

2. 5 T

3. 20 T

4. 40 T

Q.

A long, vertical wire carrying a current of 10 A in the upward direction is placed in a region where a horizontal magnetic field of magnitude $2.0\times {10}^{-3}T$ exits from south to north. Find the point where the resultant magnetic field is zero.

Q. Two infinite length wires carries currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point P(0, 0, d)m will be

1. 
2. 
3. 
4. 

Q. 96.The flux of magnetic field through a closed conducting loop of resistance 0.4 changes with time according to the equation = 0.20t2 + 0.40t + 0.60 where t is time in seconds. Find (i) the induced emf at t = 2s. (ii) the average induced emf in t = 0 to t = 5 s. (iii) charge passed through the loop in t = 0 to t = 5s (iv) average current in time interval t = 0 to t = 5 s (v) heat produced in t = 0 to t = 5s.

Q.

A long, straight wire carrying a current of 1.0 A. is placed horizontally in a uniform magnetic field $B=1.0\times {10}^{-5}T$ pointing vertically upward (figure 35-E1). Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0 cm from the wire in the same horizontal plane.

Q.

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below :

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in
(i) stable equilibrium and (ii) unstable equilibrium?

1. (1) and (3), respectively
2. (2) and (3), respectively
3. (1) and (2), respectively
4. (2) and (4), respectively

Q. (a) Write using Biot-Savart law, the expression for the magnetic field $\overrightarrow{B}$ due to an element $\overrightarrow{dl}$ carrying current I at a distance $\overrightarrow{r}$ from it in vector form.
Hence derive the expression for the magnetic field due to a current carrying loop of radius R at a point P distant X from its centre along the axis of the loop.

(b) Explain how Biot-Savart law enables one to express the Ampere's circuital law in the integral form, viz.,
$\oint \overrightarrow{B}.\overrightarrow{dl}={\mu }_{0}I$
Where I is the total current passing through the surface.