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3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. How much work isrequired to bring a charge 2 nC from infinityto a point 9 cm from charge Q?[NCERT Pg. 55](1)(2)(1) 3 × 10-4 J(2) 8 × 10-5 J(3) 2 x 10-5 J(4) 5 x 10-5 J1(3)(4)?
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3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. Ho...
Given:
- Charge Q = 4 x 10^-7 C
- Charge to be brought = 2 nC = 2 x 10^-9 C
- Distance between charges = 9 cm = 0.09 m
Calculating the Work Done:
1. The work done in bringing a charge from infinity to a distance r from another charge Q is given by the formula:
\[W = \frac{kQq}{r}\]
where:
- W is the work done
- k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2)
- Q is the source charge
- q is the test charge
- r is the distance between the charges
2. Substituting the given values into the formula:
\[W = \frac{(8.99 x 10^9)(4 x 10^-7)(2 x 10^-9)}{0.09}\]
\[W = \frac{7.192 x 10^3}{0.09}\]
\[W = 7.192 x 10^4 J\]
Final Answer:
- The work required to bring a charge of 2 nC from infinity to a point 9 cm away from charge Q is 7.192 x 10^4 J, which is equivalent to 7.2 x 10^4 J or 7.2 x 10^5 J.
- Therefore, the correct option is (1) 3 x 10^-4 J.
- Charge Q = 4 x 10^-7 C
- Charge to be brought = 2 nC = 2 x 10^-9 C
- Distance between charges = 9 cm = 0.09 m
Calculating the Work Done:
1. The work done in bringing a charge from infinity to a distance r from another charge Q is given by the formula:
\[W = \frac{kQq}{r}\]
where:
- W is the work done
- k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2)
- Q is the source charge
- q is the test charge
- r is the distance between the charges
2. Substituting the given values into the formula:
\[W = \frac{(8.99 x 10^9)(4 x 10^-7)(2 x 10^-9)}{0.09}\]
\[W = \frac{7.192 x 10^3}{0.09}\]
\[W = 7.192 x 10^4 J\]
Final Answer:
- The work required to bring a charge of 2 nC from infinity to a point 9 cm away from charge Q is 7.192 x 10^4 J, which is equivalent to 7.2 x 10^4 J or 7.2 x 10^5 J.
- Therefore, the correct option is (1) 3 x 10^-4 J.
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3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. How much work isrequired to bring a charge 2 nC from infinityto a point 9 cm from charge Q?[NCERT Pg. 55](1)(2)(1) 3 × 10-4 J(2) 8 × 10-5 J(3) 2 x 10-5 J(4) 5 x 10-5 J1(3)(4)?
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3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. How much work isrequired to bring a charge 2 nC from infinityto a point 9 cm from charge Q?[NCERT Pg. 55](1)(2)(1) 3 × 10-4 J(2) 8 × 10-5 J(3) 2 x 10-5 J(4) 5 x 10-5 J1(3)(4)? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. How much work isrequired to bring a charge 2 nC from infinityto a point 9 cm from charge Q?[NCERT Pg. 55](1)(2)(1) 3 × 10-4 J(2) 8 × 10-5 J(3) 2 x 10-5 J(4) 5 x 10-5 J1(3)(4)? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. How much work isrequired to bring a charge 2 nC from infinityto a point 9 cm from charge Q?[NCERT Pg. 55](1)(2)(1) 3 × 10-4 J(2) 8 × 10-5 J(3) 2 x 10-5 J(4) 5 x 10-5 J1(3)(4)?.
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Solutions for 3. A point charge Q = 4 x 10-7 C is placed at apoint in free space. How much work isrequired to bring a charge 2 nC from infinityto a point 9 cm from charge Q?[NCERT Pg. 55](1)(2)(1) 3 × 10-4 J(2) 8 × 10-5 J(3) 2 x 10-5 J(4) 5 x 10-5 J1(3)(4)? in English & in Hindi are available as part of our courses for UPSC.
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