1
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1 As shown in the figure, a current of $2 \mathrm{~A}$ flowing in an equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$. The magnetic field at the centroid $\mathrm{O}$ of the triangle is (Neglect the effect of earth's magnetic field)

A
$4 \sqrt{3} \times 10^{-4} \mathrm{~T}$
B
$4 \sqrt{3} \times 10^{-5} \mathrm{~T}$
C
$3 \sqrt{3} \times 10^{-5} \mathrm{~T}$
D
$\sqrt{3} \times 10^{-4} \mathrm{~T}$
2
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1 A current carrying rectangular loop PQRS is made of uniform wire. The length $P R=Q S=5 \mathrm{~cm}$ and $P Q=R S=100 \mathrm{~cm}$. If ammeter current reading changes from I to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{P Q}^I: f_{P Q}^{2 t}\right)$ is: A
1 : 4
B
1 : 3
C
1 : 2
D
1 : 5
3
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
4
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
$$\mathrm{N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=4 \mathrm{~N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$$
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