Four charges are placed at the vertices of a square of side 5 . 00 cm , as shown in the diagram. Calculate the value of the electric potential at the centre of the square (use K = 9 × 10 9 .)

The given problem is shown in the below figure From the figure, the distance between each charge and the point at the centre of the square is half the length of the diagonal of the square. The distance between each charge and the centre of the square is 5 2 cm . So, the net potential at the centre is V n e t = k q 1 r + k q 2 r + k q 3 r + k q 4 r = k r q 1 + q 2 + q 3 + q 4 V n e t = 9 × 10 9 5 2 × 10 - 2 4 + 2 - 1 - 3 × 10 - 6 V n e t = 5 . 1 × 10 5 V

Four charges are placed at the vertices of a square of side 5 . 00 cm , as shown in the diagram. Determine the work that must be done in order to move a charge of 1 nC initially at infinite to the centre of the square. (use K = 9 × 10 9 .)

The given problem is shown in the below figure From the figure, the distance between each charge and the point at the centre of the square is half the length of the diagonal of the square. The distance between each charge and the centre of the square is 5 2 cm . So, the net potential at the centre is V n e t = k q 1 r + k q 2 r + k q 3 r + k q 4 r = k r q 1 + q 2 + q 3 + q 4 V n e t = 9 × 10 9 5 2 × 10 - 2 4 + 2 - 1 - 3 × 10 - 6 V n e t = 5 . 1 × 10 5 V The work done to move a charge from the infinite to the centre of the square is W = q ∆ V W = q V c e n t r e - V i n f i n i t e = q V c e n t r e Here, V ∞ = 0 because at infinite r = ∞ V c e n t r e = 5 . 1 × 10 5 V So, W = 1 × 10 - 9 × 5 . 1 × 10 5 = 5 . 1 × 10 - 4 J

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Four equal charges $5.0 μc$ are placed at the vertices of a square side of $10 cm$ .

Determine the electric field at the centre of the square.

Important Questions on Fields (HL)

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Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 11

Four equal charges $5.0 μc$ are placed at the vertices of a square side of $10 cm$ .

How do you reconcile your answer to $a$ part question and $b$ part question with the fact that the electric field is the derivative of the electric potential $?$

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Diploma

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Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 12

A charge

q

10.0 C

is somewhere placed in the space. What is the work required to bring a charge of

1.0 mC

from a point

X

10.0 m

from

q

, to a point

Y

2.0 m

from

q

?

Does the answer depend on which path the charge follows

?

(use

K = 9 \times 10^{9}

)

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Diploma

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Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 13

An electron is bought from infinity to a distance of

10.0 cm

from a charge of

- 10.0 C

. How much work was done on the electron

?

(use

K = 9 \times 10^{9}

HARD

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 14

An electron is moving from the point

A

here the potential is

100.0 V

to point

B

where the potential is

200.0 V

. The electron started from rest. Calculate the speed of the electron as it passes from point

B

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Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 15

Four charges are placed at the vertices of a square of side $5.00 cm$ , as shown in the diagram.

Question Image

On a copy of the diagram, show the forces acting on $2.0 μC$ charge. Find the magnitude and the direction of the net force on the $2.0 μC$ charge. (use $K = 9 \times 10^{9}$ .)

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Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 15

Four charges are placed at the vertices of a square of side $5.00 cm$ , as shown in the diagram.

Question Image

Calculate the value of the electric potential at the centre of the square (use $K = 9 \times 10^{9}$ .)

HARD

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 15

Four charges are placed at the vertices of a square of side $5.00 cm$ , as shown in the diagram.

Question Image

Determine the work that must be done in order to move a charge of $1 nC$ initially at infinite to the centre of the square. (use $K = 9 \times 10^{9}$ .)

HARD

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 10 - Fields (HL)>Test yourself>Q 16

Two conducting spheres are separated by a distance that is large compared with their radii. The first sphere has a radius of $10.0 cm$ and has a charge of $2.00 μC$ on its surface. The second sphere has a radius of $15.0 cm$ and is neutral. The spheres are then connected by a long conducting wire.

Find the charges on each sphere.

Four equal charges 5.0 μc are placed at the vertices of a square side of 10 cm. Determine the electric field at the centre of the square.

Important Questions on Fields (HL)

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Four equal charges $5.0 μc$ are placed at the vertices of a square side of $10 cm$ .

Determine the electric field at the centre of the square.