Which one of the following expressions represents Biot-Savart's law? Symbols have their usual meanings.

1. \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \hat r)}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\\ \) 2. \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \hat r)}{4 \pi|\overrightarrow{\mathrm{r}}|^2} \)
3. \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \vec{r})}{4 \pi|\vec{r}|^3} \) 4. \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\)

Subtopic:  Biot-Savart Law |
 68%
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A charged particle is projected through a region in a gravity-free space. If it passes through the region with constant speed, then the region may have:
1. \(\vec{E}=0, \vec{B} \neq 0\)
2. \(\vec{E} \neq 0, \vec{B} \neq 0\)
3. \(\vec{E} \neq 0, \vec{B}=0\)
4. Both (1) & (2)

Subtopic:  Lorentz Force |
 61%
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A neutron, a proton, an electron and an \(\alpha\text-\)particle enter a region of the uniform magnetic field with the same velocity. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure. Which track will the \(\alpha\text-\)particle follow?
             

1. \(A\) 2. \(B\)
3. \(C\) 4. \(D\)
Subtopic:  Lorentz Force |
 59%
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On connecting a shunt of \(10 ~ \Omega,\) the deflection in a moving coil galvanometer falls from 40 divisions to 6 divisions. What is the resistance of the galvanometer?

1.  \(\frac{120}{3}~\Omega \) 2. \(\frac{30}{7}~\Omega \)
3. \(\frac{170}{3}~\Omega \) 4. \(\frac{150}{7}~\Omega \)
Subtopic:  Conversion to Ammeter & Voltmeter |
 68%
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Magnetic field at the outer surface of long hollow cylindrical shells of radius R and carrying current I is B. What is the magnetic field at a distance of 3R2 from the axis of the cylindrical shell?

1. \(B \over 2\) 2. \(2B\)
3. \(B \over 4\) 4. \(2B \over 3\)
Subtopic:  Ampere Circuital Law |
 85%
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If a long hollow copper pipe carries a direct current along its length, then the magnetic field associated with the current will be:

1. Only inside the pipe 2. Only outside the pipe
3. Both inside and outside the pipe 4. Zero everywhere
Subtopic:  Ampere Circuital Law |
 78%
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As indicated, a long, straight conductor XY carrying a current i1 is placed antiparallel to a conductor AB of length l carrying a current i2. How much of a force is acting on AB?

   

1. μ0i1i2

2.  μ0i1i2π

3. μ0i1i22π

4. 2μ0i1i2

Subtopic:  Force between Current Carrying Wires |
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An electron and a proton are revolving around a common centre O in two coplanar circular paths as shown in the figure with a time period of rotation of 1 s and 2 s, respectively. What will be the net magnetic field at O?

1. \(\frac{\mu _{0}e}{\pi }\) tesla.
2. \(\frac{\mu _{0}e}{2}\) tesla.
3. \(2\mu _{0}e\) tesla.
4. zero.

Subtopic:  Magnetic Field due to various cases |
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What is the magnetic moment of the following current loop?
 
1. 24 Am2

2. 12 Am2

3. 6 Am2

4. Zero

Subtopic:  Magnetic Moment |
 73%
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The two parts of the loop are circles of radii 2a and a, respectively, and carry the same current i as shown in the given figure. What is the magnitude of the dipole moment of the current loop?

     

1. 5πa2 i

2. 4πa2 i

3. 3πa2 i

4. Zero

Subtopic:  Magnetic Moment |
 71%
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