1
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

A massless square loop, of wire of resistance $$10 \Omega$$, supporting a mass of $$1 \mathrm{~g}$$, hangs vertically with one of its sides in a uniform magnetic field of $$10^{3} \mathrm{G}$$, directed outwards in the shaded region. A dc voltage $$\mathrm{V}$$ is applied to the loop. For what value of $$\mathrm{V}$$, the magnetic force will exactly balance the weight of the supporting mass of $$1 \mathrm{~g}$$ ?

(If sides of the loop $$=10 \mathrm{~cm}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$$)

A
1 V
B
$$\frac{1}{10}$$V
C
10 V
D
100 V
2
JEE Main 2023 (Online) 30th January Morning Shift
+4
-1

The magnetic moments associated with two closely wound circular coils $$\mathrm{A}$$ and $$\mathrm{B}$$ of radius $$\mathrm{r}_{\mathrm{A}}=10$$ $$\mathrm{cm}$$ and $$\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$$ respectively are equal if : (Where $$\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$$ and $$\mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}}$$ are number of turn and current of $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively)

A
$$4 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$
B
$$2 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$
C
$$\mathrm{N}_{\mathrm{A}}=2 \mathrm{~N}_{\mathrm{B}}$$
D
$$\mathrm{N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=4 \mathrm{~N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$
3
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

A
2 T
B
4 T
C
8 T
D
16 T
4
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

The magnitude of magnetic induction at mid point $$\mathrm{O}$$ due to current arrangement as shown in Fig will be

A
$$\frac{\mu_{0} I}{\pi a}$$
B
$$\frac{\mu_{0} I}{4 \pi a}$$
C
$$\frac{\mu_{0} I}{2 \pi a}$$
D
0
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