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Question

Calculate the potential difference between points A and B in an electric field E=(2^i+3^j+4^k) NC1, where the position vectors of points A and B are rA=(^i2^j+^k) m and rB=(2^i+^j2^k) m respectively.

A
4 V
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B
3 V
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C
2 V
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D
1 V
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Solution

The correct option is D 1 V
Given,
Position vector of point A,
rA=(^i2^j+^k) m
Position vector of point B,
rB=(2^i+^j2^k) m
The relation between electric field (E) and electric potential difference (dV) is given by
dV=E.dr
where, dr=dx^i+dy^j+dz^k

The potential difference between point A and B is
ABdV=ABE.dr

ABdV=(1,2,1)(2,1,2)(2^i+3^j+4^k).(dx^i+dy^j+dz^k)

ABdV=(1,2,1)(2,1,2)(2dx+3dy+4dz)

VAVB=[[2x]12+[3y]21+[4z]12]

VAVB=[2(12)+3(21)+4(1+2)]

VAVB=[29+12]=1V

Hence, option (d) is correct answer.

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