Electric Field and Charge Particle in Electric Field

Q 11 :
A small bob of mass 100 mg and charge +10 C is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' $σ$ ' as shown in figure. If string subtends an angle of 45° with the sheet at equilibrium the charge density of sheet will be:

(Given, $ε_{0} = 8.85 \times 10^{- 12} \frac{F}{m}$ and acceleration due to gravity, $g = 10 m / s^{2}$ ) [2025]

0.885 $nC / m^{2}$
17.7 $nC / m^{2}$
885 $nC / m^{2}$
1.77 $nC / m^{2}$

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(4)

T sin 45° = Eq

T cos 45° = mg

$E = \frac{m g}{q} = \frac{σ}{2 ε_{0}}$

$σ = \frac{2 ε_{0} m g}{q} = 1.77 nC / m^{2}$

Q 12 :
Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

$\frac{a}{\sqrt{2}}$
$\frac{a}{2}$
a
0

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(3)

$E = K \frac{Q r}{{(x^{2} + R^{2})}^{3 / 2}}$

For $E_{\max} = \frac{d E}{d x} = 0$

$∴ x = \frac{R}{\sqrt{2}} = \frac{\sqrt{2} a}{\sqrt{2}} = a$

Q 13 :
A metallic ring is uniformly charges as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

2 E
$\sqrt{2} E$
E/2
Zero

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(2)

Q 14 :
Given below are two statements: one is lavelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning strikes.

Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.

In the light of the above statements, chose the most appropriate answer from the options given below: [2025]

Both (A) and (R) correct and (R) is the correct explanation of (A)
(A) is correct but (R) is not correct
Both (A) and (R) correct but (R) is not the correct explanation of (A)
(A) is not correct but (R) is correct

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(1)

The outer body of aircraft is made with metal to provide electrostatic shielding such that electric field inside craft remain zero for any charge on outer surface.

Q 15 :

Electric charge is transferred to an irregular metallic disk as shown in figure. If $σ_{1}, σ_{2}, σ_{3}$ and $σ_{4}$ are charge densities at given points then, choose the correct answer from the options given below: [2025]

(A) $σ_{1} > σ_{3}; σ_{2} = σ_{4}$

(B) $σ_{1} > σ_{2}; σ_{3} > σ_{4}$

(C) $σ_{1} > σ_{3} > σ_{4} = σ_{2}$

(D) $σ_{1} > σ_{2}; σ_{3} = σ_{4}$

(E) $σ_{1} = σ_{2} = σ_{3} = σ_{4}$

A, B and C Only
A and C Only
D and E Only
B and C Only

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(1)

$σ \infty \frac{1}{R} R \to radius of curvature$

$R_{2} = R_{4} > R_{3} > R_{1}$

$\Rightarrow σ_{1} > σ_{3} > σ_{4} = σ_{2}$

Topic Question Set

Q 12 :
Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

Q 13 :
A metallic ring is uniformly charges as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

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Topic Question Set

Q 12 : Consider a circular loop that is uniformly charged and has a radius a2. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

Q 13 : A metallic ring is uniformly charges as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

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Q 12 :
Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

Q 13 :
A metallic ring is uniformly charges as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]