1
JEE Main 2021 (Online) 27th July Morning Shift
+4
-1
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$$\theta$$' with the vertical?
A
$$x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 2}}}$$
B
$$x = {\left( {{{{q^2}l} \over {2\pi {\varepsilon _0}mg}}} \right)^{{1 \over 3}}}$$
C
$$x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}g}}} \right)^{{1 \over 3}}}$$
D
$$x = {\left( {{{{q^2}{l^2}} \over {2\pi {\varepsilon _0}{m^2}{g^2}}}} \right)^{{1 \over 3}}}$$
2
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$$^\circ$$ with the axis. The ratio of the dipole moment of A and B, $${{{p_1}} \over {{p_2}}}$$ is : (take $$\sin 37^\circ = {3 \over 5}$$)

A
$${3 \over 8}$$
B
$${3 \over 2}$$
C
$${2 \over 3}$$
D
$${4 \over 3}$$
3
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $$\times$$ 10$$-$$6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.
A
0.485 mC
B
815.1 nC
C
8.8 $$\mu$$C
D
4.44 $$\mu$$C
4
JEE Main 2021 (Online) 20th July Morning Shift
+4
-1
A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m2. At every point the direction of current density is at an angle of 60$$^\circ$$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is :

(Resistivity of magnesium $$\rho$$ = 44 $$\times$$ 10$$-$$8 $$\Omega$$m)
A
11 $$\times$$ 10$$-$$5 V/m
B
11 $$\times$$ 10$$-$$3 V/m
C
11 $$\times$$ 10$$-$$7 V/m
D
11 $$\times$$ 10$$-$$2 V/m
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