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Chapter 11: Problem 1547

Two uniformaly charged spherical conductors \(\mathrm{A}\) and \(\mathrm{B}\) having radius \(1 \mathrm{~mm}\) and \(2 \mathrm{~mm}\) are separated by a distance of \(5 \mathrm{~cm} .\) If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres \(\mathrm{A}\) and \(\mathrm{B}\) is..... (A) \(4: 1\) (B) \(1: 2\) (C) \(2: 1\) (D) \(1: 4\)

Short Answer

Expert verified
The ratio of the magnitude of the electric fields at the surfaces of spheres A and B is \(2:1\).

Step by step solution

01

Understanding the equilibrium condition

In equilibrium condition, the potential of conductors connected by a conductor remains the same. For spheres A and B, this means that the potential on A is equal to the potential on B. Therefore, we have: \(ER_{A} = ER_{B}\) or \(E_{A} = \frac{R_{B}}{R_{A}}E_{B}\) (1)
02

Calculate the ratio of the electric fields

The ratio of the magnitude of the electric fields at the surfaces of spheres A and B can be calculated by substituting the radius of sphere A \(R_{A}=1mm\) and B \(R_{B}=2mm\) into equation (1). The result is \(E_{A}/E_{B} = \frac{2mm}{1mm} = 2\). The correct choice is (C) \(2: 1\). So, the ratio of the electric fields at the surfaces of the two spheres (A and B) is \(2:1\). This suggests that the electric field at the surface of sphere A is twice as strong as that at the surface of sphere B. This is due to the smaller radius of sphere A, which results in a stronger electric field.

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Most popular questions from this chapter

The electric Potential \(\mathrm{V}\) at any Point $0(\mathrm{x}, \mathrm{y}, \mathrm{z}\( all in meters \))\( in space is given by \)\mathrm{V}=4 \mathrm{x}^{2}\( volt. The electric field at the point \)(1 \mathrm{~m}, 0.2 \mathrm{~m})\( in volt meter is \)\ldots \ldots .$ (A) 8 , along negative \(\mathrm{x}\) - axis (B) 8 , along positives \(\mathrm{x}\) - axis (C) 16 , along negative \(\mathrm{x}\) -axis (D) 16 , along positives \(\mathrm{x}\) -axis

An electric dipole is placed along the \(\mathrm{x}\) -axis at the origin o. \(\mathrm{A}\) point \(P\) is at a distance of \(20 \mathrm{~cm}\) from this origin such that OP makes an angle \((\pi / 3)\) with the x-axis. If the electric field at P makes an angle \(\theta\) with the x-axis, the value of \(\theta\) would be \(\ldots \ldots \ldots\) (A) \((\pi / 3)+\tan ^{-1}(\sqrt{3} / 2)\) (B) \((\pi / 3)\) (C) \((2 \pi / 3)\) (D) \(\tan ^{-1}(\sqrt{3} / 2)\)

If an electron moves from rest from a point at which potential is 50 volt, to another point at which potential is 70 volt, then its kinetic energy in the final state will be \(\ldots .\) (A) \(1 \mathrm{~N}\) (B) \(3.2 \times 10^{-18} \mathrm{~J}\) (C) \(3.2 \times 10^{-10} \mathrm{~J}\) (D) 1 dyne

Two Points \(P\) and \(Q\) are maintained at the Potentials of \(10 \mathrm{v}\) and \(-4 \mathrm{v}\), respectively. The work done in moving 100 electrons from \(\mathrm{P}\) to \(\mathrm{Q}\) is \(\ldots \ldots \ldots\) (A) \(2.24 \times 10^{-16} \mathrm{~J}\) (B) \(-9.60 \times 10^{-17} \mathrm{~J}\) (C) \(-2.24 \times 10^{-16} \mathrm{~J}\) (D) \(9.60 \times 10^{-17} \mathrm{~J}\)

Point charges \(4 \mu \mathrm{c}\) and \(2 \mu \mathrm{c}\) are placed at the vertices \(\mathrm{P}\) and Q of a right angle triangle \(P Q R\) respectively. \(Q\) is the right angle, \(\mathrm{PR}=2 \times 10^{-2} \mathrm{~m}\) and \(\mathrm{QR}=10^{-2} \mathrm{~m}\). The magnitude and direction of the resultant electric field at \(\mathrm{R}\) is \(\ldots \ldots\) (A) \(4.28 \times 10^{9} \mathrm{NC}^{-1}, 45^{\circ}\) (B) \(2.38 \times 10^{8} \mathrm{NC}^{-1}, 40.9^{\circ}\) (C) \(1.73 \times 10^{4} \mathrm{NC}^{-1}, 34.7^{\circ}\) (D) \(4.9 \times 10^{10} \mathrm{NC}^{-1}, 34.7^{\circ}\)
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