03. Inductance (Self and Mutual Induction)
Electro Magnetic Induction

154948 A proton of velocity $(3 \hat{i}+2 \hat{j}) \mathrm{ms}^{-1}$ enters a field of magnetic induction $(2 \hat{j}+3 \hat{k}) T$, the acceleration produced in the proton in $\mathrm{ms}^{-2}$ is (specific charge of proton $=0.96 \times 10^{8} \mathrm{C}-\mathrm{kg}^{-1}$ )

1 $2.8 \times 10^{8}(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})$
2 $2.88 \times 10^{8}(2 \hat{i}-3 \hat{j}+2 \hat{k})$
3 $2.8 \times 10^{8}(2 \hat{i}+3 \hat{k})$
4 $2.88 \times 10^{8}(\hat{i}-3 \hat{j}+2 \hat{k})$
Electro Magnetic Induction

154949 A wire in the form of a square of side a carries a current $i$. Then, the magnetic induction at the centre of the square is (magnetic permeability of free space $=\mu_{0}$ )

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{a}}$
2 $\frac{\mu_{0} \mathrm{i} \sqrt{2}}{\pi \mathrm{a}}$
3 $\frac{2 \sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}}$
4 $\frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{a}}$
Electro Magnetic Induction

154950 A long straight wire carrying a current of $30 \mathrm{~A}$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \mathrm{~T}$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \mathrm{~cm}$ away from the wire is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $10^{-4}$
2 $3 \times 10^{-4}$
3 $5 \times 10^{-4}$
4 $6 \times 10^{-4}$
Electro Magnetic Induction

154951 Two parallel rails of a railway track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is $1 \mathrm{~m}$. A train is travelling with a velocity of $72 \mathrm{kmh}^{-1}$ along the track. The reading of the millivoltmeter (in $\mathrm{mV}$ ) is (vertical component of the earth's magnetic induction is $2 \times 10^{-5} \mathrm{~T}$ )

1 1.44
2 0.72
3 0.4
4 0.2
Electro Magnetic Induction

154948 A proton of velocity $(3 \hat{i}+2 \hat{j}) \mathrm{ms}^{-1}$ enters a field of magnetic induction $(2 \hat{j}+3 \hat{k}) T$, the acceleration produced in the proton in $\mathrm{ms}^{-2}$ is (specific charge of proton $=0.96 \times 10^{8} \mathrm{C}-\mathrm{kg}^{-1}$ )

1 $2.8 \times 10^{8}(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})$
2 $2.88 \times 10^{8}(2 \hat{i}-3 \hat{j}+2 \hat{k})$
3 $2.8 \times 10^{8}(2 \hat{i}+3 \hat{k})$
4 $2.88 \times 10^{8}(\hat{i}-3 \hat{j}+2 \hat{k})$
Electro Magnetic Induction

154949 A wire in the form of a square of side a carries a current $i$. Then, the magnetic induction at the centre of the square is (magnetic permeability of free space $=\mu_{0}$ )

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{a}}$
2 $\frac{\mu_{0} \mathrm{i} \sqrt{2}}{\pi \mathrm{a}}$
3 $\frac{2 \sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}}$
4 $\frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{a}}$
Electro Magnetic Induction

154950 A long straight wire carrying a current of $30 \mathrm{~A}$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \mathrm{~T}$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \mathrm{~cm}$ away from the wire is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $10^{-4}$
2 $3 \times 10^{-4}$
3 $5 \times 10^{-4}$
4 $6 \times 10^{-4}$
Electro Magnetic Induction

154951 Two parallel rails of a railway track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is $1 \mathrm{~m}$. A train is travelling with a velocity of $72 \mathrm{kmh}^{-1}$ along the track. The reading of the millivoltmeter (in $\mathrm{mV}$ ) is (vertical component of the earth's magnetic induction is $2 \times 10^{-5} \mathrm{~T}$ )

1 1.44
2 0.72
3 0.4
4 0.2
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Electro Magnetic Induction

154948 A proton of velocity $(3 \hat{i}+2 \hat{j}) \mathrm{ms}^{-1}$ enters a field of magnetic induction $(2 \hat{j}+3 \hat{k}) T$, the acceleration produced in the proton in $\mathrm{ms}^{-2}$ is (specific charge of proton $=0.96 \times 10^{8} \mathrm{C}-\mathrm{kg}^{-1}$ )

1 $2.8 \times 10^{8}(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})$
2 $2.88 \times 10^{8}(2 \hat{i}-3 \hat{j}+2 \hat{k})$
3 $2.8 \times 10^{8}(2 \hat{i}+3 \hat{k})$
4 $2.88 \times 10^{8}(\hat{i}-3 \hat{j}+2 \hat{k})$
Electro Magnetic Induction

154949 A wire in the form of a square of side a carries a current $i$. Then, the magnetic induction at the centre of the square is (magnetic permeability of free space $=\mu_{0}$ )

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{a}}$
2 $\frac{\mu_{0} \mathrm{i} \sqrt{2}}{\pi \mathrm{a}}$
3 $\frac{2 \sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}}$
4 $\frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{a}}$
Electro Magnetic Induction

154950 A long straight wire carrying a current of $30 \mathrm{~A}$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \mathrm{~T}$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \mathrm{~cm}$ away from the wire is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $10^{-4}$
2 $3 \times 10^{-4}$
3 $5 \times 10^{-4}$
4 $6 \times 10^{-4}$
Electro Magnetic Induction

154951 Two parallel rails of a railway track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is $1 \mathrm{~m}$. A train is travelling with a velocity of $72 \mathrm{kmh}^{-1}$ along the track. The reading of the millivoltmeter (in $\mathrm{mV}$ ) is (vertical component of the earth's magnetic induction is $2 \times 10^{-5} \mathrm{~T}$ )

1 1.44
2 0.72
3 0.4
4 0.2
Electro Magnetic Induction

154948 A proton of velocity $(3 \hat{i}+2 \hat{j}) \mathrm{ms}^{-1}$ enters a field of magnetic induction $(2 \hat{j}+3 \hat{k}) T$, the acceleration produced in the proton in $\mathrm{ms}^{-2}$ is (specific charge of proton $=0.96 \times 10^{8} \mathrm{C}-\mathrm{kg}^{-1}$ )

1 $2.8 \times 10^{8}(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})$
2 $2.88 \times 10^{8}(2 \hat{i}-3 \hat{j}+2 \hat{k})$
3 $2.8 \times 10^{8}(2 \hat{i}+3 \hat{k})$
4 $2.88 \times 10^{8}(\hat{i}-3 \hat{j}+2 \hat{k})$
Electro Magnetic Induction

154949 A wire in the form of a square of side a carries a current $i$. Then, the magnetic induction at the centre of the square is (magnetic permeability of free space $=\mu_{0}$ )

1 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{a}}$
2 $\frac{\mu_{0} \mathrm{i} \sqrt{2}}{\pi \mathrm{a}}$
3 $\frac{2 \sqrt{2} \mu_{0} \mathrm{i}}{\pi \mathrm{a}}$
4 $\frac{\mu_{0} \mathrm{i}}{\sqrt{2} \pi \mathrm{a}}$
Electro Magnetic Induction

154950 A long straight wire carrying a current of $30 \mathrm{~A}$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4} \mathrm{~T}$. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point $2.0 \mathrm{~cm}$ away from the wire is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $10^{-4}$
2 $3 \times 10^{-4}$
3 $5 \times 10^{-4}$
4 $6 \times 10^{-4}$
Electro Magnetic Induction

154951 Two parallel rails of a railway track insulated from each other and with the ground are connected to a millivoltmeter. The distance between the rails is $1 \mathrm{~m}$. A train is travelling with a velocity of $72 \mathrm{kmh}^{-1}$ along the track. The reading of the millivoltmeter (in $\mathrm{mV}$ ) is (vertical component of the earth's magnetic induction is $2 \times 10^{-5} \mathrm{~T}$ )

1 1.44
2 0.72
3 0.4
4 0.2