SATHEE: Electrostatics 3 Question 17

Electrostatics 3 Question 17

17. A spherical metal shell $A$ of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{B} (< R_{A})$ are kept far apart and each is given charge $+ Q$ . Now they are connected by a thin metal wire. Then

(a) $E_{A}^{inside} = 0$

(b) $Q_{A} > Q_{B}$

(d) $E_{A}^{on surface} < E_{B}^{on surface}$

(2011)

Show Answer

Answer:

Correct Answer: 17. (a, b, c, d)

Solution:

Inside a conducting shell electric field is always zero. Therefore, option (a) is correct. When the two are connected, their potentials become the same.

$∴ V_{A} = V_{B} or \frac{Q_{A}}{R_{A}} = \frac{Q_{B}}{R_{B}} V = \frac{1}{4 π ε_{0}} \frac{Q}{R}$

Since, $R_{A} > R_{B} ∴ Q_{A} > Q_{B}$

$∴$ Option (b) is correct.

Potential is also equal to, $V = \frac{σ R}{ε_{0}}, V_{A} = V_{B}$

$∴ σ_{A} R_{A} = σ_{B} R_{B}$ or $\frac{σ_{A}}{σ_{B}} = \frac{R_{B}}{R_{A}}$ or $σ_{A} < σ_{B}$

$∴$ Option (c) is correct.

Electric field on surface, $E = \frac{σ}{ε_{0}}$ or $E \propto σ$

Since, $σ_{A} < σ_{B} ∴ E_{A} < E_{B}$

$∴$ Option (d) is also correct

$∴$ Correct options are (a), (b), (c) and (d).

Electrostatics 3 Question 17

17. A spherical metal shell $A$ of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{B} (< R_{A})$ are kept far apart and each is given charge $+ Q$ . Now they are connected by a thin metal wire. Then

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Electrostatics 3 Question 17

17. A spherical metal shell A of radius RA and a solid metal sphere B of radius RB(<RA) are kept far apart and each is given charge +Q. Now they are connected by a thin metal wire. Then

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

17. A spherical metal shell $A$ of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{B} (< R_{A})$ are kept far apart and each is given charge $+ Q$ . Now they are connected by a thin metal wire. Then