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Question

A cube has sides of length l=0.2 m. It is placed with one corner at the origin as shown in figure. The electric field is uniform and given by E=(2.5^i4.2^j) N/C. Find the electric flux through the entire cube.


A
Zero
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B
10 N-m2/C
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C
15 N-m2/C
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D
5 N-m2/C
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Solution

The correct option is A Zero
Given:
l=0.2 m;
E=(2.5^i4.2^j) N/C

We know that, electric flux through any surface is given by,
ϕ=E.A

For left surface (1) of cube,
A1=(0.04 ^j) m2 [A=l2=0.22 m2=0.04 m2]

So, ϕ1=E.A1=(2.5^i4.2^j).(0.04^j)=0.168 N-m2/C

Similarly, for right surface (2),

ϕ2=0.168 N-m2/C

for front surface (3),

ϕ3=0.1 N-m2/C

for back surface (4),

ϕ4=0.1 N-m2/C

for top surface (5) of cube,
A5=(0.04 ^k) m2

So, ϕ5=E.A5=(2.5^i4.2^j)(0.04^k)=0

ϕ5=0

Similarly, for bottom surface (6),

ϕ6=0

Now, net electric flux through entire cube

ϕnet=ϕ1+ϕ2+ϕ3+ϕ4+ϕ5+ϕ6

ϕnet=0.168+(0.168)+0.1+(0.1)+0+0=0

Hence, option (d) is correct.

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