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Question
In a certain region static electric and magnetic fields exist. The magnetic feild is given by →B=B0(^i+2^j−4^k) . If a test charge is given by →v=v0(3^i+^j−2^k) experiences no force in that region, then the electric field in the region, in SI units, is :
In a certain region static electric and magnetic fields exist. The magnetic feild is given by →B=B0(^i+2^j−4^k) . If a test charge is given by →v=v0(3^i+^j−2^k) experiences no force in that region, then the electric field in the region, in SI units, is :
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Solution
The correct option is B →E=−v0B0(14^j+7^k)
→B=B0(i+2j−4^k)→v=v0(3i−j)+2k)Now, →B×→v=B0v0(−^k−2j−6^k+4^i−12^j−4^j)=B0v0(0^j−14^j−7^k)=−B0v0(14^j+7^k)
→B=B0(i+2j−4^k)
→v=v0(3i−j)+2k)
Now,
→B×→v=B0v0(−^k−2j−6^k+4^i−12^j−4^j)
=B0v0(0^j−14^j−7^k)
=−B0v0(14^j+7^k)
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